Fill a large soup pot with water. Wash, peel and cut the potatoes into about 1-inch cubes.
Cover the potatoes with water by an inch at the top.
Bring to a boil over high heat and maintain a simmer 20-25 minutes until the potatoes are fork tender.
Drain well and add back to the pot.
Add 4 tablespoons butter, 1 teaspoon salt, ¼ teaspoon black pepper and the half & half.
Mash with a potato masher until there are no lumps left. Taste and season again with more salt and pepper if needed.
Stir in the cheese and chives followed by 3 egg yolks. Allow the potatoes to cool off about 20 minutes.
Line 2 large baking sheets (or 3 medium - they must fit in your freezer) with parchment paper.
Scoop up the potatoes by ½ cups and mound them onto the baking sheets forming them into circles.
Use the back of a round tablespoon to form a well in the center of each one.
Combine the remaining egg yolk with the tablespoon of half & half. Brush each one lightly with the mixture using a pastry brush.
Place the baking sheets, one at a time if they don't both fit, in the freezer 20 - 25 minutes.
Meanwhile preheat the oven to 450 degrees F.
Bake the potatoes 15 - 18 minutes or until golden brown. If they melt a little and lose some of their shape use the backs of two spoons to push them back into shape as soon as you take them out of the oven.
Let the potatoes rest 10 minutes.
To serve: cut the remaining butter into pats and place one in the center of each potato.