Make the sauce by combining the olive oil, single cream, balsamic vinegar, salt and pepper. Beat until the mixture becomes a proper emulsion.
Slice the apple (that you can then keep in a bowl of lemon water to prevent it from turning brown), fine slices of fennel, slices of avocado and slices of Reblochon.
Layer your millefeuilles by alternating slices of apple, slices of Reblochon, slices of speck, slices of avocado, slices of fennel and finish off with some Reblochon and speck.
Add some snipped chives and some of the sauce, and serve immediately.