Heat a large skillet over medium heat and add 2 tablespoons of olive oil along with 2 tablespoons of butter. Once melted, toss in 1 chopped onion, 1 chopped carrot, and 1 chopped celery stalk, stirring occasionally for about 5-7 minutes until the vegetables soften and become fragrant.

Increase the heat to medium-high and add 1 pound of ground beef into the skillet with the softened vegetables. Using a wooden spoon, break the meat apart as it cooks for about 8-10 minutes until browned and no pink remains.

Stir in one 28-ounce can of crushed tomatoes, 1 cup of beef broth, 2 tablespoons of tomato paste, and 1 teaspoon each of dried oregano, salt, and pepper. Reduce the heat to low, letting the sauce simmer uncovered for 30 minutes, stirring occasionally until it thickens.

In a separate saucepan, melt 4 tablespoons of butter over medium heat. Whisk in 4 tablespoons of flour to form a roux, cooking it for 1-2 minutes. Gradually add 3 cups of milk while whisking continuously, allowing the mixture to thicken for approximately 5-7 minutes until creamy.

Preheat your oven to 375°F (190°C).

In a deep baking dish, start with a layer of meat sauce, then place cooked lasagna noodles over it. Spoon some béchamel sauce on top, followed by a sprinkling of grated Parmigiano-Reggiano cheese. Repeat this layering process, finishing with a final layer of béchamel and a generous topping of cheese.

Cover the baking dish with aluminum foil and place it in the preheated oven. Bake for 40-45 minutes, then remove the foil for the last 10 minutes to allow the top to brown beautifully.

Once out of the oven, let the lasagna rest for about 10 minutes before slicing.