Trim the green end of the leek and discard. Cut the leek in half lengthwise and wash in between the layers. Slice the leek. Melt 1 tablespoon butter in a large saute pan over medium heat and saute the sliced leeks until softened, about 4-5 minutes. Season with salt and pepper and remove from heat. Let cool slightly.
Combine the leeks with 4 cups grated butternut squash, gruyere, 1 egg, 1 teaspoon salt, and ½ teaspoon black pepper until well combined. Heat 1 tablespoon oil in the same saute pan over medium heat. Scoop ⅓ cup of the butternut squash mixture and place it on the pan to form a round "pancake." Repeat with the remaining mixture. Cook until golden brown, about 3 minutes. Flip and cook on the other side until browned. Remove from heat and cook the rest of the butternut squash.
Meanwhile, make the dill creme fraiche. Beat together ½ cup creme fraiche with 1 teaspoon fresh chopped fill and 1 teaspoon dijon mustard. Season with salt and pepper.
Fry 4 eggs until the desired degree of doneness.
Arrange the butternut squash rosti on a platter. Place a dollop of the dill creme fraiche on top followed by a fried egg. Sprinkle red pepper flakes on top and garnish with fresh dill. Serve immediately.