Place tomatoes in a colander or on rack in sink to allow juices to drain. Salt them to help release juices.
In a small bowl, mix goat cheese, mayonnaise and chives. Set aside.
Roll premade dough into an 11-inch oval or circle on floured surface. This is a free-form pie baked on a sheet. If it is too hard to roll because butter has firmed too much, let sit on counter for about 15 minutes. (You can also roll it on a Silpat baking mat or a piece of parchment paper that can be easily transferred to your baking sheet).
Spread goat cheese mixture onto dough, leaving an edge of about 2 inches. Arrange tomatoes on top of that. (The tomatoes may look high but they will cook down.) Sprinkle the flour over the top of tomatoes. This will soak up excess liquid.
Fold the dough over just to the edge of the tomatoes. It will not cover them completely but will make an edge. Brush it with half-and-half and sprinkle edge with salt and pepper.
Bake 1 hour and 10 minutes. Let stand at room temperature for at least an hour before cutting.