Preheat the oven to 180°C (350°F).
Peel and thinly slice the shallot.
Heat the olive oil in a pan or skillet and golden brown the shallot. Add the sugar and stir. Immediately add the tomatoes, salt, and chili, and cook for about 5 minutes.
Stir enough to coat the tomatoes with the syrup. Add the balsamic vinegar, stir and cook for a minute.
Transfer the tomatoes and their liquids to the cake pan. Add the basil, coarsely chopped.
Cover with the pie crust and use your fingers to fit it through the sides of the pan, wrapping up the tomatoes.
Bake in the oven 25-30 minutes, until the crust turns golden brown.
Let temperature decrease a bit, then flip the pie, after losing the edges with the help of a spatula.
Serve the tomato galette hot or cold accompanied by fresh mozzarella or other delicate flavor cheeses.