Bring a large pot of salted water to a rolling boil. Add lasagna noodles and cook until al dente, about 8-10 minutes. Drain and toss with olive oil.

In a medium saucepan, melt butter over medium heat. Stir in flour to create a roux for 2 minutes. Gradually whisk in milk and cook until thickened, about 5-7 minutes. Mix in the pesto.

In a mixing bowl, combine ricotta, Parmesan, egg, dried basil, and garlic powder. Season with salt and pepper, mixing until well blended.

In a baking dish, spread a thin layer of pesto béchamel sauce, followed by a layer of noodles, cheese mixture, and mozzarella. Repeat, ending with a layer of noodles topped with béchamel and mozzarella.

Cover the dish with foil and bake at 375°F for 50 minutes. Remove foil and bake for an additional 10-15 minutes until golden brown. Let rest for 15 minutes before serving.