Make the croutons: Preheat oven to 400 degrees. Toss bread cubes with oil, salt, pepper and garlic powder. Place in the oven and bake for 15 to 20 minutes.
Make the salad: Using a sharp knife, thinly slice the Brussel sprouts. Place in a large bowl and add salt and lemon juice. Gently massage the Brussel sprouts for about 2 minutes, until wilted.
For the dressing: Place the capers and garlic on top of each other on a cutting board. Chop and mash together until a paste forms. Whisk the egg yolk, mustard and lemon juice in a bowl. Drop by drop add the oil while whisking to emulsify. Add a little water if needed to thin out. Stir in garlic and caper mixture.
To assemble: Add croutons, cheese, and dressing to Brussel sprouts and toss well.