Position an oven rack in the upper third of your oven and preheat to 450°F.

Make the Pickled Grapes: In a small saucepan, combine white wine vinegar, 1 tablespoon kosher salt, sugar, and water. Bring to a simmer and heat until salt and sugar completely dissolve. Place sliced grapes in a heatproof bowl and pour the pickling liquid over them. Set aside, stirring occasionally, for 10 minutes. Drain pickling liquid from grapes, stir in ¼ teaspoon kosher salt and chopped tarragon and transfer to the refrigerator until ready to serve.

Make the Garlic Parmesan Butter: In a small bowl, mix together softened butter, 1 tablespoon grated Parmesan, garlic powder, ¼ teaspoon salt, and red pepper flakes.

Place pizza crust on a baking sheet and spread the butter mixture in an even layer over the top, leaving an inch or so around the perimeter of the crust. Tear mozzarella slices in half and place over the top of the butter, leaving a little space between each piece. Top with a scattering of sliced shallots and freshly cracked black pepper.

Bake pizza in preheated oven until the cheese melts, about 7-10 minutes. Switch to broil and cook until cheese is bubbly and browned, about 1-2 minutes more, rotating the baking sheet if the cheese isn't browning evenly.

To serve, transfer pizza to a pizza peel or cutting board. Sprinkle with freshly shaved Parmesan cheese, torn pieces of prosciutto, and the pickled grapes. Tear fresh burrata cheese over top right before serving.