Divide the pastry in half. Roll out half the pastry to an 11-inch (27.5cm) circle and fit it into a 9-1/2 inch (24cm) removable bottom tart pan, leaving the pastry hanging over the edges of the tart pan. Roll out the remaining pastry to a 9-1/2 inch (24cm) round. Refrigerate the prepared tart pan and the round of pastry.
Place the olive oil in a large, heavy-bottomed skillet over medium heat. Add the pepper strips and the onion, toss so they are coated with oil, and cook until the peppers are tender and the liquid they exude has almost all evaporated, about 17 minutes. Add the garlic, season lightly with salt, stir, and cook, partially covered, until the garlic has melted into the peppers and onion, and the peppers are completely tender, about 50 minutes. Adjust the seasoning and remove from the heat. Let cool to room temperature.
Preheat the oven to 425 F (220 C).
Remove the prepared tart pan and the round of pastry from the refrigerator and turn the pepper and tomato mixture into it, smoothing it out so it is in an even layer. Place the round of pastry atop the pepper and tomato mixture, and bring the edges of the bottom pastry over the edges of the top pastry. Press the pastry edges gently together then crimp them so they are attractive. Poke several holes in the top of the pastry and place the tart on a baking sheet.
Bake the tart in the center of the oven until the pastry is golden and cooked through, 30 to 35 minutes. Remove the tart from the oven, remove the ring from the tart pan, and let the tart cool on a wire rack for at least 10 minutes. Transfer the tart from the tart pan to a serving platter, and serve.