To make the beurre blanc, add the shallots, vinegar, and wine to a saucepan.
Simmer over medium heat until it is reduced by more than half, about 5 minutes.
Add the cream.
Add the butter chunks to the pan all at once.
Turn the heat to high and whisk while moving the pan until it has completely melted.
Season with salt and pepper.
Strain out the shallots.
To make the pea puree, boil 2 cups of water and add the garlic clove. Cook the peas until tender, about 3 minutes. Remove garlic clove. Add to the blender with pesto, salt, and pepper. Pulse until you get a consistency you like. Use a little of the cooking water to thin if necessary. Remove from the blender and mix in Parmesan.
To sear the scallops, pat the scallops dry with a paper towel. Season with salt and pepper. Heat a saute pan over high heat. Add butter and oil. Place scallops in the pan.
Leave them alone for about a minute and a half on each side, they will develop a golden crust.
To plate, add pea puree to a plate. Top with scallops and pour beurre blanc on top. (Beurre blanc recipe from Saveur.)