Combine Capers (2 tablespoon) with Olive Oil (2 tablespoon) in a small pot over medium heat. Fry the capers for a few minutes until shrivelled up and crispy (it may splatter a bit at the end). Drain then set aside.
Grate the Garlic (2 clove). Cube the Unsalted Butter (1/2 cup) and set aside.
Pass the Yukon Gold Potato (1/2 cup) through a ricer, to get it as finely mashed as you can (if you don't have a ricer, crush/rub it between your fingers to make sure there are no lumps), then transfer to a small pot.
Add Dijon Mustard (1 1/2 tablespoon), Egg (1), and grated Garlic. Whisk with a fork until evenly whipped.
Hold the pot close to a medium-low flame to keep warm (but not enough to cook the ingredient), then add a couple cubes of unsalted butter whisking until melted and incorporated before adding the next.
If the butter has trouble melting, just bring the pot closer to the flame to warm up. Continue until all the butter's been incorporated. If you want to be really anal for that tongue-wrapping silkiness, pass the sauce through a fine sieve.
Last, add the fried capers and season with Sea Salt (to taste) as needed.
This goes superbly with grilled fish, roasted chicken or roasted vegetables.