2 cups flour, plus more for dusting
1½ cups shredded sharp cheddar cheese
10 tbsp. unsalted butter, cubed and chilled
1½ tsp. kosher salt, plus more to taste
½ tsp. freshly ground black pepper, plus more to taste
⅓ cup ice-cold water
3 medium vine-ripe tomatoes, cored and sliced ¼" thick
⅓ cup grated pecorino cheese
¼ cup mayonnaise
2 scallions, thinly sliced
2 tbsp. finely chopped basil