Pulse together the cornmeal, sweet rice flour, oat flour, tapioca starch, xanthan gum, and salt in the bowl of a food processor. (If you don't have a food processor, you can whisk by hand).

Add the thyme and cold butter, but don't pulse. One tablespoon at a time, dribble ice water into the food processor, pulsing after each addition, until the dough holds together when pinched with your fingers. Add water until it just holds together, but is not sticky. If you need more water, add a teaspoon at a time. (If working by hand, mix the butter into the flour with your hands, breaking up the butter until the largest pieces are about the size of a pea. Mix in ice water, one tablespoon at a time, until the dough just holds together).

Form the dough into a flat disc and wrap in plastic. Refrigerate for 30 minutes to an hour.

Meanwhile, prepare the filling as directed below.

Lightly flour a piece of parchment paper with cornmeal and place the dough on top. With a second piece of parchment paper on top, roll the rough into a 13-inch round that will fit in your tart pan (If you don't have a tart pan, you can do it free form by folding the edges up over the filling like a galette). Remove the top piece of parchment paper and flip the round over into the tart pan, pressing down on the bottom and sides. Carefully peel back the second piece of parchment paper and trim/press the edges. Chill for 10 minutes.

Preheat the oven to at 400ºF.

Spread the tomato slices out on a paper-towel lined baking sheet and sprinkle ½ teaspoon of salt over the top. Flip the tomatoes and sprinkle the other side with another ½ teaspoon of salt. Let sit for at least 15 minutes, but as long as an hour. Pat dry.

Mix the ricotta, 3 ounces of the feta, egg, thyme, ¼ teaspoon salt, and pepper until smooth (it's okay if the feta is a little clumpy). Chill while you prepare the pesto (below).

Spread ⅓ cup of the arugula walnut pesto into a thin even layer on top of the chilled tart crust.

Spread the chilled ricotta over the pesto and smooth out with a spatula.

Layer the sliced tomatoes over the ricotta filling.

Crumble the remaining feta over the tomatoes and sprinkle parmesan over the top.

Bake the tart until the crust and cheese are golden, about 50 minutes. Top with fresh thyme leaves and serve with dollops of pesto

Place all of the ingredients together in a food processor and purée until smooth.

Taste and adjust salt, if needed.