Preheat oven to 375 degrees F (190 degrees C). Line 2 baking sheets with parchment paper.
Arrange butternut squash slices in a single layer on each baking sheet. Drizzle 1 tablespoon of olive oil over each layer; season each with 1 teaspoon Italian seasoning, salt, and pepper.
Bake in the preheated oven until squash is soft but still firm to the bite, about 15 minutes.
Heat a large skillet over medium heat; cook and stir beef and garlic until browned, about 5 minutes. Drain grease. Mix in remaining 1 teaspoon Italian seasoning, pasta sauce, brown sugar, basil, and 1 1/2 teaspoon salt. Simmer, stirring occasionally, until flavors combine, about 10 minutes.
Mix remaining 1 teaspoon salt, ricotta cheese, eggs, 1/2 cup Parmesan cheese, and parsley together in a bowl.
Layer 1/3 of the squash slices in the bottom of a 9x13-inch baking dish. Cover squash with 1/2 of the ricotta mixture, 1/2 of the mozzarella cheese and 1/3 of the beef mixture. Repeat layers, ending with remaining squash slices and sauce. Sprinkle 2 tablespoons Parmesan cheese on top.
Bake in the preheated oven until cheeses are melted and sauce is bubbly, about 30 minutes. Let stand for 10 minutes before serving.