For the beef tartare: Finely chop the steak with a chef's knife. Add to a bowl along with the olive oil, piment d'Espelette, chives, salt and pepper. Mix well and set aside.
For the cheese: Finely grate the Gruyere using a rasp grater. Spread out on a rimmed baking sheet and allow to dry for 1 hour.
For the French onion dip: Add the olive oil to a medium skillet over medium heat, followed by the onions. Cook until brown and caramelized, stirring often and adding a few tablespoons of water if the skillet gets too dry, about 25 minutes. Cool the onions completely.
Place the onions in a blender along with the sour cream, salt and pepper. Blend until smooth. Set aside.
For the crispy onions: Heat the canola oil to 375 degrees F in a large Dutch oven.
Add the sliced onions and buttermilk to a bowl and soak for 5 minutes. Add the flour to a second bowl, then use a spider to remove the onions from the buttermilk and toss them in the flour, coating them well. Fry in batches until golden brown and crispy, 3 to 4 minutes. Remove with a slotted spoon and drain on paper towels. Season with salt.
Place the beef tartare loosely on a platter. Spoon the onion dip on the side. Garnish with the crispy onions. Sprinkle with the dried Gruyere. Cut the endive into individual leaves for scooping and serve on the side.