Preheat the oven to 400 degrees F. Line a baking sheet with parchment.
Arrange the bacon in a single layer on the baking sheet. Bake until crispy, 25 to 30 minutes. Remove to a cutting board.
Add the butternut squash to the baking sheet. Sprinkle with 1/2 teaspoon salt and a few cracks black pepper. Toss the squash until it is fully coated in the bacon fat and spices. Bake until the squash is tender, 15 to 20 minutes. Set aside. Leave the oven on.
Meanwhile, spray a 9-by-13-inch baking dish with nonstick cooking spray.
Melt the butter in a medium saucepan over medium-high heat. Add the leeks and cook, stirring occasionally, until softened and starting to brown, 2 to 3 minutes. Add the thyme, paprika and garlic and cook for 1 minute more. Season with salt and pepper.
Pour in the chicken stock and 2 cups water. Use a wooden spoon to scrape up any remaining browned bits. Bring to a boil and slowly add the polenta, stirring constantly with a wooden spoon. Continue to cook, stirring frequently, until the polenta is thickened and cooked, about 5 minutes. Stir in 1 teaspoon salt and 1/2 teaspoon pepper, then taste for seasoning. Whisk together the eggs and 1/2 cup of the Parmesan in a bowl or measuring cup. Whisk the egg mixture into the polenta, then pour the polenta into the prepared baking dish.
Chop the bacon and mix it into the squash. Spoon the squash and bacon evenly over the polenta, then use a spatula or your hands to press it into the warm polenta. Top with the remaining 1/2 cup Parmesan. Bake until set and brown on top, 15 to 20 minutes. Let cool to room temperature, then cut into squares and serve as finger food.