Crispy shallots: Pour vegetable oil into a medium pot. Using a mandolin, slice shallots into thin rounds and separate with fingers. Place flour in bowl, add shallots and toss until well coated and dry to prevent sticking. Shake off excess flour, then add to cold oil. Heat the oil over medium-high heat until shallots start to bubble; reduce to medium.
Cook shallots, stirring often to avoid them sticking to the bottom, until golden and crispy. Remove using slotted spoon, place on paper-towel-lined plate and sprinkle with a pinch of salt.
Bagna càuda: In a small pot, add anchovies, garlic and olive oil and heat over low until the garlic is sweet and without colour and the anchovies have melted down. Pour into a blender and purée; add the butter a few cubes at a time, with the motor running, until blended and incorporated. Scrape into bowl.
Assembly: In large bowl, toss chicory with lemon juice to coat. Arrange and layer leaves standing in 2 shallow serving bowls; using a spoon, drizzle bagna càuda over chicory before adding the next layer. Sprinkle with Parmesan, espelette and shallots.