Make the Danish Remoulade: Combine all ingredients in a small bowl and stir until fully combined
Heat grill. Grill hot dogs over medium heat until heated through and nicely browned, about 7-10 minutes
Place one hot dog inside of each bun. Spoon Danish Remoulade over the length of the hot dog, followed by pickled cucumbers and a sprinkle of crispy shallots. Serve immediately.