Pulse flour, cheese, sugar, salt and butter in a food processor until mixture resembles coarse meal. Add the egg yolk and pulse to combine. With the processor running, drizzle in 1/4 cup of cold water until dough comes together, adding more if necessary. Wrap dough in plastic wrap and let rest in the refrigerator for 30 minutes.

Heat 1 tbsp of olive oil in a medium skillet over medium high heat. Add the shallot and cook, stirring occasionally, until softened, about 3 minutes. Add the kale and cook, stirring occasionally until just beginning to wilt. Transfer to a large bowl.

Halve one-third of the tomatoes. Add to the large bowl with the remaining whole tomatoes, cheeses, basil, lemon juice, flour and sugar. Season with salt and pepper and toss gently to combine.

Roll out the dough on a lightly floured surface to a 13 inch circle. Lay dough over a 10 inch pie plate. Drizzle the dough with the remaining 1 tbsp of olive oil and add the filling. Fold up the edges of the dough over the filling leaving a hole in the center. Add extra tomatoes if using. Refrigerate for 20 minutes.

Preheat oven to 375. Brush the crust with olive oil and bake until golden brown, about 45 minutes.