Step 1
Place a rack in middle of oven; preheat to 350°. Heat 1 Tbsp. extra-virgin olive oil in a large Dutch oven or other heavy pot over medium-high. Cook 1 lb. ground beef (20% fat) and 8 oz. hot Italian sausage, casings removed, breaking up into small pieces with a wooden spoon, until well browned and cooked through, 10–12 minutes. Using a slotted spoon, transfer meat to a medium bowl, leaving fat behind.
Step 2
Add 2 large onions, finely chopped, 6 garlic cloves, finely chopped, and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt to same pot; if pot looks dry, add up to 1 Tbsp. more oil. Cook, stirring often, until onions are translucent and golden around the edges, 8–10 minutes. Add 2 Tbsp. double-concentrated tomato paste and 1 Tbsp. dried oregano; cook, stirring constantly, until paste is brick red and beginning to stick to bottom of pot, 5–8 minutes. Return meat to pot.
Step 3
Add one 28-oz. can plus one 14.5-oz. can crushed tomatoes, ¼ cup Worcestershire sauce, 1 tsp. sugar, and 1 tsp. freshly ground pepper to pot. Bring to a simmer, stirring occasionally and scraping up any browned bits stuck to bottom of pot. Remove from heat and stir in 2 oz. Parmesan, finely grated (about 1 cup). Taste tomato sauce and season with more salt if needed.
Step 4
Toss 12 oz. Fontina cheese, grated (about 3 cups), and remaining 4 oz. Parmesan, finely grated (about 2 cups), in a large bowl to combine; measure out 1 cup cheese and set aside for topping. Add 2 large eggs, 24 oz. whole-milk cottage cheese, and remaining 2 garlic cloves, finely chopped, 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt, and 1 tsp. freshly ground pepper to remaining cheese in bowl. Mix vigorously with a wooden spoon until combined.
Step 5
Arrange 3 regular dried lasagna noodles in a single layer in a 13×9″ baking dish. (If noodles are long, arrange parallel to long sides of baking dish; if noodles are short, arrange parallel to short sides of baking dish. Don’t worry about any gaps—noodles will swell as they cook.) Spread 1½ cups tomato sauce over noodles. Scatter one third of Fontina mixture evenly over sauce (mixture will be stiff; use hands to break off small pieces and scatter over sauce). Starting with another layer of noodles, repeat process, creating 4 layers of noodles in total and ending with a layer of tomato sauce. Top lasagna with reserved cheese.
Step 6
Place baking dish on a large rimmed baking sheet (to catch drips) and bake lasagna until sauce is bubbling around the edges, top is golden brown, and noodles are al dente (insert a skewer into center of lasagna to check), 75–85 minutes. Let sit at least 15 minutes and up to 45 minutes before serving.
Do Ahead: Lasagna can be baked 2 days ahead. Let cool completely; cover loosely with foil and chill. Reheat, covered, in a 325° oven until warmed through, 30–45 minutes.
