Place Bob's Red Mill Gluten Free Pie Crust Mix in a bowl or food processor fitted with a steel blade. Cut in butter using a pastry blender or two knives until crumbly or give the food processor ten 1-second pulses. Add 1/2-cup cheddar cheese and mix or pulse briefly just to combine. Add water gradually and mix until the dough sticks together, adding additional water if needed. Divide dough in half and flatten into disks. Wrap tightly in plastic wrap and refrigerate for at least 1 hour.
Slice tomatoes into rounds 1/4 - 1/2-inch thick. Sprinkle with 1 tsp salt and let sit on a few layers of paper towels for 15 minutes. Combine 1 cup grated Cheddar cheese and mayonnaise in a small bowl; set aside.
Remove dough from the refrigerator and let sit at room temperature until malleable. Preheat oven to 425°F and line a baking sheet with parchment paper. To form pies, roll prepared Bob's Red Mill Gluten Free Pie Crust with Cheddar between two sheets of parchment or heavy-duty plastic wrap to 1/8-inch thickness and cut eight 8 1/2-inch rounds (reroll the dough as necessary). Carefully transfer one round to a parchment lined baking sheet. Assemble each pie one-at-a-time on the baking sheet.
In the center of each pie round layer one tomato slice and sprinkle with chopped basil. Make sure to leave a large 1 1/2-inch border. Repeat with another tomato slice and basil then top with about 1 1/2 Tbsp of the cheese-mayonnaise mixture.
Carefully fold the edges of the dough over the filling in small sections, overlapping the edges as you go. Leave about 2-inches of filling exposed in the center of the pie. Try not to move the formed pies as they are very delicate. When all pies are assembled, transfer the baking sheet to the freezer for at least 1 hour.
To bake the pies, preheat the oven to 425°F. Thoroughly whisk together 1 egg and 1 Tbsp water. Brush the crust of each frozen pie with the eggwash.
Bake the pies until the crust is golden and the filling is beginning to bubble, 30 - 35 minutes. Let cool at least 5 minutes before serving. Serve warm or at room temperature.