Preheat the oven to 350°F (175°C). Lightly grease a 9x13-inch baking dish.
Cook the lasagna noodles according to package directions until al dente. Drain and set aside.
In a large bowl, mix the ricotta cheese, beaten eggs, sour cream, and herb and garlic soup mix until smooth and well combined.
In a separate bowl, combine the thawed broccoli, sliced carrots, and corn kernels. Mix gently.
Stir the condensed cream of mushroom soup into the ricotta mixture until fully incorporated.
Spread a thin layer of the ricotta-soup mixture on the bottom of the baking dish.
Arrange a layer of cooked lasagna noodles over the mixture, slightly overlapping.
Spread half of the vegetable mixture evenly over the noodles.
Spoon and spread about half of the ricotta-soup mixture over the vegetables.
Sprinkle with one cup of shredded Cheddar cheese and about half a cup of Parmesan cheese.
Repeat the layers: noodles, remaining vegetables, remaining ricotta-soup mixture, and cheeses.
Finish with a final layer of noodles topped with the remaining shredded Cheddar and Parmesan cheeses.
Cover the dish with foil and bake for 30 minutes.
Remove the foil and bake uncovered for an additional 15 minutes, or until the cheese is melted and bubbly.
Let the lasagna rest for 10 minutes before slicing and serving.