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 grated butternut squash, gruyere, egg, salt, and 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 creme fraiche with fresh chopped fill and 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.
Notes
For a simpler side dish, you can omit the fried eggs and enjoy the butternut squash rosti with just the dill creme fraiche.