To make the dough, mix together the flour, polenta, sugar, and salt in the bowl of a stand mixer fitted with the paddle attachment, or make it by hand by putting the dry ingredients in a medium bowl (and use a pastry blender or your fingers to mix the dough).
Add the cubed, cold butter and mix until the pieces of butter are the size of large corn kernels.
Add the water and continue to mix until the dough starts to come together.
Use your hands to gather the dough and shape it into a disk. If the dough feels too dry to do that, add more water, ½ tablespoon at a time, until it comes together.
Wrap the dough in plastic wrap or your favorite eco-friendly alternative and chill for at least an hour. (The dough can be made up to 3 days in advance.)
To make the tart, remove the dough from the refrigerator. Unwrap it and, holding the disk of dough perpendicular to the counter, rap the sides of the dough on the counter, turning it as you go, to soften the edges.
On a lightly floured countertop, roll the dough out to a 14-inch circle, turning the dough and sprinkling more flour on the counter and the dough to keep it from sticking.
Place the dough on a baking sheet lined with parchment paper or a silicone baking mat.
Preheat the oven to 400ºF (200ºC) while you assemble the tart.
Spread a layer of mustard on the dough, leaving a few inches empty around the perimeter.
Slice the tomatoes about ⅓-inch thick and layer them in concentric circles over the mustard.
Sprinkle the tomatoes with a little salt and freshly ground pepper.
Fold the edges of the dough over the tomatoes to make an outer crust.
Place chunks of ricotta cheese over and partially tucked under the tomatoes.
Brush the edges of the dough with melted butter and grate Parmesan cheese over the entire tart.
Bake until the tomatoes are soft and cooked through and the crust is dark golden brown, about 35-40 minutes.
Slide the tart off the pan onto a wire rack and let cool for about ten minutes before serving.
