Spinach and Squash Lasagna - Fresh-Pressed Olive Oil

Ingredients

• 5 tablespoons extra virgin olive oil, divided use, plus more for drizzling
• 2 pounds whole squash or 1 3/4 pounds precut chunks
• Freshly ground black pepper
• Fine sea salt
• 3/4 pound fresh or 1 pound dry regular or no-boil lasagna sheets
• 16 ounces whole milk ricotta
• 2 large eggs
• 1 3/4 cups freshly grated Parmigiano-Reggiano, divided use
• Pinch of pepperoncini (crushed red pepper flakes), plus more to taste
• 1/8 teaspoon freshly grated nutmeg, or to taste
• 1 tablespoon finely chopped fresh sage, about 3 large leaves
• 2 garlic cloves, grated on a microplane
• 1 pound fresh spinach, rinsed, patted dry, and coarsely chopped
• 6 ounces fontina, grated, about 1 3/4 cups