Preheat oven to 375º F. Spray a 9”x 13” by 2”(or more) deep baking dish with non-stick cooking spray.
Heat a large skillet over medium heat and add ½ Tbsp of the olive oil. Add minced onions and sauté for 2 minutes.
Add shredded zucchini and yellow squash to the skillet and ¼ tsp of the salt. Sauté for 5 minutes, stirring frequently and transfer to a strainer set over a medium bowl to drain and cool. (Do not discard the liquid that drains from the zucchini, it will be used in the assembly of the lasagna.)
Add ½ Tbsp of olive oil to the now empty skillet and sauté the shredded carrots for 5 minutes over medium low heat until just beginning to get tender. Remove from skillet to a small bowl and let cool.
Wipe any carrot reside from the skillet with a damp cloth and return to the stovetop over medium heat. Add 4 Tbsp of butter to the skillet and let melt before sprinkling with the all purpose flour. Stir flour into the melted butter until it forms a paste.
Cook flour butter paste for 1 minute to form a roux.
Reduce heat to medium low. While whisking, add cold milk to the hot roux one cup at a time, whisking thoroughly between each addition. (The mixture will be very thick after the first addition, but just keep adding milk and whisking and it will reach the correct consistency.)
Simmer the béchamel over medium low heat for about five minutes until it begins to thicken. Remove the skillet from the heat and whisk in 6 Tbsp (50 grams) of the parmesan cheese, 1 ½ tsp of the salt and ⅛ tsp of the pepper. Cover the cheese sauce and set aside.
In a medium, microwave safe, bowl melt 2 Tbsp of butter in the microwave. Add the 2 remaining Tbsp of olive oil and stir to combine.
Add the panko breadcrumbs and the 2 remaining Tbsp of grated parmesan cheese to the bowl with the olive oil and melted butter and toss until the breadcrumbs are completely coated. Sprinkle the breadcrumbs with ½ tsp of salt, ⅛ tsp of pepper and ¼ tsp of dried thyme and toss thoroughly. Set aside.
In a large bowl place the ricotta cheese, drained sautéed zucchini, carrots, minced fresh basil and 1 tsp of salt and lightly beaten eggs. Gently stir together until completely combined.

Assembly:

Place 3 Tbsp of the reserved zucchini liquid in the bottom of your prepared baking dish and top with 3 sheets of Barilla No-Boil lasagna noodles.
Spread ½ of the ricotta mixture on top of the noodles making sure to spread evenly to the edges of the baking dish.
Reserve 3 Tbsp of the shredded cheddar cheese for the top layer and sprinkle half of the remaining cheddar cheese over the first layer of the ricotta mixture.
Drizzle 1 cup of the béchamel cheese sauce evenly over the cheese.
Repeat with another 3 sheets of noodle, the remaining ricotta mixture, second half of shredded cheddar and another 1 cup of béchamel cheese sauce.
Finally, add the last 3 sheets of lasagna noodles, and press down gently to make sure the lasagna is level across. Pour on the remaining béchamel cheese sauce and spread evenly over the top. Sprinkle with the reserved cheddar cheese. Sprinkle the breadcrumb mixture evenly over the surface of the lasagna.
Spray a sheet a aluminum foil with cooking spray and cover the baking dish (sprayed side down) crimping it tightly around the rim.
Place the baking dish on a sheet tray and transfer to the center of your preheated oven.
Bake covered for 45 minutes at 375º F. Remove the aluminum foil and bake for an addition 30 minutes uncovered until the top is golden brown and the center registers 180º F on an instant read thermometer.
Remove from oven and let stand for 20 minutes before slicing and serving!

To Make Ahead:

Assemble the whole lasagna, but do not prepare the breadcrumb topping. Press a sheet of plastic wrap onto the surface of the béchamel cheese sauce, cover the top of the baking dish with an additional layer of plastic wrap and refrigerate for up to 24 hours. When ready to bake, remove plastic wrap. Prepare the breadcrumb topping and sprinkle evenly over the surface of the lasagna. Bake as instructed, but add 10-15 to the covered baking time to account for the cold temperature of the refrigerated lasagna.

To Reheat:

Place as many slices of cold lasagna as desired on a parchment-lined baking sheet that’s been sprayed with cooking spray. Space slices at least 2” apart. Cover the tray with aluminum foil and crimp tightly around edges to seal. Bake in the center of a preheat 350ºF oven for 30 minutes until center of the lasagna pieces reaches 165ºF. Enjoy!

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