Preheat the oven to 400F.
Heat the butter in a frying pan. When the froth dissipates, add the beef and spread over the bottom of the pan. Cook without disturbing until the underside is browned. Stir, breaking up lumps, and continue cooking until the meat loses its raw appearance.
Sprinkle in the cumin, oregano and thyme. Add salt and pepper. Cook, stirring often, until the mixture is almost dry. Taste and add more salt and pepper, as needed. Set aside the beef to cool.
Make the white sauce. In the same pan where the beef was cooked, melt the remaining 1/4 cup of butter. Add the flour all at once and stir to remove lumps. Cook over medium heat for three to four minutes. Pour the milk in a thin stream, stirring as you pour. Cook the white sauce until thickened. Season with salt and pepper.
Assemble the dish. Spread about two tablespoons of the white sauce on the entire bottom of an 8"x8" baking dish.
Arrange the lasagne on top of the white sauce (tip: cut the noodles to fit the pan).
Scatter a third of the ground beef over the noodles.
Pour a third of the white sauce over the meat.
Take a third of the pesto and drop by teaspoonfuls over the white sauce.
Spread a third of the shredded cheese over the layers of noodles, meat and sauces.
Repeat the layering procedure until you have three layers of everything.
Bake the lasagne with pesto and white sauce at 400F until bubbly and the top is lightly browned, about 20 minutes.
Rest the baked lasagne for about ten minutes before cutting and serving.