For the roasted tomatoes:
Preheat oven to 225 degrees F. Slice tomatoes in half. Add tomatoes and garlic to a non-reactive (read: non-aluminum) baking dish or a baking sheet lined with parchment. Drizzle with olive oil, salt and pepper. Bake for 3 hours.
For the piadina:
Mix together flour, salt, and baking powder in a bowl, then stir in oil and water. Knead dough for several minutes, until smooth. (If you are using all all-purpose flour, this may take up to 10 minutes. If you are using half spelt flour, you can knead it for slightly less time and it doesn't have to be perfectly smooth).
Cover dough in plastic wrap and let rest at room temperature for an hour. (The dough can also be prepared ahead of time and refrigerated for several days).
Lightly flour a surface for rolling and roll out the dough until as thin as you like (it should be quite thin, about a 1/4 to 1/10 of an inch (it will puff up slightly as it cooks).
Cut out circles of your desired size--I used a 6-inch cake pan as a template and ran a knife around the edge.
Make sure you have the rest of your ingredients ready before you start cooking the piadina! Heat a frying pan over medium-high heat. Once hot, add the circle of dough and let cook for 30-60 seconds, or until brown spots start to form on the bottom. Prick the piadina all over with a fork to help the middle cook, then flip and cook for another 30 seconds. Immediately assemble your grilled cheese while the piadina is still warm.
Peel the roasted garlic and smear a few cloves on a piadina. Add a few slices of gruyere cheese, a generous handful of roasted tomatoes and some basil on top. Grill over medium heat until cheese is melted. Eat immediately.