Thaw one pastry sheet, and roll it out into a 12-inch square on a lightly floured surface. Preheat the oven to 400˚ F and line a baking sheet with parchment paper. Using a sharp knife or pizza wheel, slice four strips, each 1-inch wide from the pastry, and place them along the edges of the pastry sheet. It will look like the frame around a picture when you're done. Light press them down. Dock the pastry with a fork, meaning poke the pastry sheet (not the frame) a bunch of times with a fork.
Bake for 15 minutes or until crisply browned. Remove and cut a couple of slits in the baked pastry if it's bowed up in the middle, and gently press flat. Do this while it's still warm.
Slice the large tomato into 1/4" thick slices and place in a single layer on paper towels to drain for 10 - 15 minutes. Slice the cherry tomatoes in half.
Spread the artichoke spread on the bottom of the tart, completely covering it in a thin layer. If you have some left over, keep it for spreading on top of the tomatoes. Arrange the tomatoes in the tart shell in a single layer on top of the artichoke spread. Sprinkle on the cheeses, and bake for 10 - 12 minutes, or until the cheese is melted.
Finish with a little flurry of basil just before serving. Slice into 2-bite pieces using a pizza wheel, and serve warm.