Step 1

Pulse 2 cups flour and 1¼ tsp. kosher salt in a food processor to combine. Add butter and pulse until mixture resembles coarse meal with a few pea-size pieces of butter remaining.

Step 2

Transfer mixture to a large bowl; drizzle with vinegar and ¼ cup ice water. Mix with a fork, adding more ice water by the tablespoonful as needed, just until a shaggy dough comes together. Turn out onto a work surface and lightly knead until no dry spots remain (be careful not to overwork). Pat into a disk and wrap in plastic. Chill at least 2 hours.

Step 3

Preheat oven to 400°. Gently toss tomatoes, garlic, and remaining 1 tsp. kosher salt in a large bowl. Let sit 5 minutes (tomatoes will start releasing some liquid). Drain tomato mixture and transfer to paper towels.

Step 4

Unwrap dough and roll out on a lightly floured sheet of parchment paper to a 14" round about ⅛" thick. Transfer on parchment to a baking sheet. Scatter cheese over dough, leaving a 1½" border. Arrange tomatoes and garlic over cheese. Bring edges of dough up and over filling, overlapping as needed to create about a 1½" border; brush dough with egg. Sprinkle tomatoes with sea salt and pepper. Chill in freezer 10 minutes.

Step 5

Bake galette, rotating once, until crust is golden brown and cooked through, 55–65 minutes. Let cool slightly on baking sheet. Finely grate zest from lemon over galette; sprinkle with chives.

Step 6

Do Ahead: Dough can be made 2 days ahead. Keep chilled.