In a large skillet, combine the ground beef and Italian sausage. Cook over medium-high heat until browned. Drain excess grease and set aside.
In another skillet, melt goat butter with 1 tablespoon olive oil. Add the sliced onions, season with sea salt and freshly cracked black pepper, and cook until they begin to brown. Reduce the heat to low and let them slowly caramelize for 35–40 minutes, stirring occasionally, until soft, jammy, and golden. Remove from heat and set aside.
Bring a large stockpot of salted water to a boil. Add lasagna noodles and cook for 5 minutes (they'll finish cooking in the oven). Drain, then shock in an ice-water bath to stop the cooking. Keep submerged in cold water to prevent sticking.
Dice the green and red peppers, slice the green onions, and mince the garlic. You can sauté them briefly in olive oil (1–2 minutes) for a sweeter, softer flavor, or keep them fresh for crunch and brightness in the layers.
Build the Lasagna. Brush the bottom of a 9×13 baking dish with 1 tablespoon olive oil. Ladle in 2 cups of pasta sauce (this both prevents sticking and starts with flavor). Layer noodles across the bottom. Add spoonfuls of ricotta (room temperature spreads more easily). Add some of the caramelized onions. Add browned meat mixture. Spoon on more sauce. Sprinkle with mozzarella + Parmigiano. Add diced peppers, green onions, and garlic.
Repeat layers until the pan is nearly full, finishing with noodles → sauce → a heavy blanket of mozzarella + Parmigiano.
Cover loosely with foil and bake at 350°F for 45–60 minutes, or until the mixture is bubbling and golden. Remove foil for the last 10 minutes if you want a browned cheesy crust.
Remove from oven and let rest 15 minutes before cutting (so it holds together). Garnish with fresh parsley and serve with garlic bread.