Heat the olive oil in a large skillet over medium heat. Add the onion, carrot, and celery and cook until softened, about 5 minutes.
Add the ground beef and garlic. Cook until the beef is browned, breaking it up with a spoon as it cooks. Season with salt, pepper, and oregano.
Pour in the crushed tomatoes and simmer the sauce for 15 minutes until it thickens slightly. Remove from heat.
In a bowl, stir together the ricotta cheese and chopped fresh basil. Set aside.
Preheat the oven to 375°F. Spread a thin layer of Bolognese sauce in the bottom of an 8x8 baking dish.
Layer 2 noodles over the sauce, followed by one-third of the remaining sauce, one-third of the ricotta mixture, and one-quarter of the mozzarella and Parmesan. Repeat the layers two more times.
Finish with a final layer of noodles and the remaining sauce and cheeses. Cover with foil and bake for 25 minutes.
Remove the foil and bake 10 minutes more until the cheese is bubbly and lightly browned. Let the lasagna rest 10 minutes before slicing.