1 medium carrot, peeled and roughly chopped
1 medium rib celery, roughly chopped
½ small onion, roughly chopped
1 (28 oz) can whole tomatoes with juice
2 Tbsp unsalted butter
8 oz ground beef
8 oz ground pork
8 oz ground veal
1½ C whole milk
1½ C dry white wine
2 Tbsp tomato paste
1 tsp table salt
¼ tsp ground black pepper
4 Tbsp unsalted pepper
1/4 C unbleached all purpose flour
4 C whole milk
¾ tsp table salt
15 sheets no boil lasagna noodles
4 oz Parmesan cheese
Process carrot, celery and onion in food processor until finely chopped, about ten 1 second pulses, scraping down bowl as necessary; transfer mixture to small bowl. Wipe out food processor work bowl; process tomatoes and juice until finely chopped, 6-8 1-second pulses. Heat butter in a heavy bottomed Dutch oven over medium heat until foaming. Add carrots, celery, and onion and cook, stirring occasionally, until soften but not browned, about 4 min. Add ground meats and cook until brown. Add milk and stir. Bring to a simmer and cook until almost all liquid has evaporated, 20-30 min. Add wine and bring to a simmer, stir occasionally, until liquid has evaporated 20-30 min. Stir in tomato paste until combined, about 1 min. Add chopped tomatoes, salt and pepper. Bring to a simmer, then reduce heat to medium-low and cook until sauce thickened, about 15 min. (You should have about 6 cups of sauce.) Cool until it’s warm to the touch, about 30 min.
Melt butter in medium saucepan over medium heat until foaming; add flour and whisk constantly for 1½ min. Mixture should not brown. Gradually whisk in milk. Increase heat to medium-high and bring to a full boil. Whisk frequently. Add salt and reduce heat to medium-low. Simmer for 10 min. Cool to just warm, about 30 min.
Heat oven to 425º. Place noodles in a 13x9” baking dish and cover with very hot tap water, soak 5 min, agitating noodles occasionally to prevent sticking. Remove noodles from water, place in single layer on kitchen towel and pat dry. Wipe out baking dish and spray lightly with nonstick cooking spray. Stir béchamel to recombine. Mix ¾ C warm béchamel into warm meat sauce until thoroughly combined.
Distribute 1 C béchamel enriched meat sauce in baking dish. Place 3 noodles in single layer on top of sauce, arranging them close together, but not touching, at center of pan. Spread 1¼ C meat sauce evenly over noodles, spread sauce to edge of noodles but not edge of dish. Drizzle ⅓ C béchamel evenly over meat sauce. Sprinkle ⅓ C Parmesan over béchamel. Repeat layering of noodles, meat sauce, béchamel and cheese 3 more times. Place final 3 noodles on top and completely cover with remaining béchamel, spread allowing sauce and allowing it to spill over noodles. Sprinkle with remaining Parmesan.
Spray large sheet of foil with nonstick cooking spray and cover lasagna. Bale until bubbling, about 30 min. Remove foil, increase heat to 450º and continue baking until surface is spotty brown, about 15 min. Cool 15 min. Serve.