Start with the Arugula Pesto. In a food processor add hazelnuts and pulse until finely ground. Add arugula, grated Parmesan cheese, lemon zest and juice and salt and pepper.
Continue to pulse and as the pesto is blending, slowly drizzle in olive oil until desired consistency. When done, taste for seasoning and adjust as needed. Spoon pesto into sealed jar and refrigerate until ready to use.
Make the galette dough. To a clean food processor, add flour, salt and cold cubed butter and pulse until the mixture looks like small peas.
In a small bowl, whisk the Greek yogurt, lemon juice and water and add to the flour mixture and pulse until blended together. You can test the dough by squeezing a small piece of dough with your hands and f it sticks together easily, it's ready.
Using very floured hands, form dough into a disk, wrap in plastic wrap and allow to rest in the fridge for 30 minutes.
Prep the Tomatoes. Meanwhile, slice your tomatoes thin and place them on double lined paper towels. Sprinkle tomatoes with salt and cover with another sheet of paper towel. This will allows the tomatoes to release moisture so your tart won't get soggy.
Dust a clean work surface with flour and roll out dough to about a 10-12 inch circle.
Once dough is rolled out, transfer it to a non-stick baking sheet. The dough is fragile so it needs to be on the baking sheet before toppings are added. Spread a thin layer of pesto onto the dough leaving a 1 inch border around.
Layer tomato slices over the pesto, overlapping if needed.
Fold the border over and brush the dough with egg wash. Sprinkle everything with flakey salt and drizzle the tomatoes with a bit of olive oil.
Bake the tomato galette at 400 degrees Fahrenheit for 25 minutes until the crust is golden brown.
Serve warm or at room temperature.