1. Preheat the broiler on high and bring a large pot of salted water to the boil.
2. Arrange the fresh tomatoes in a single layer in a high-sided glass baking dish, then drizzle over 2 tbsp oil and the balsamic vinegar. Sprinkle over the brown sugar and season with salt and pepper, then place under the broiler while you make the pesto.
3. In the bowl of a food processor (or a large mortar and pestle, if you have one) add the basil leaves, half the pine nuts, half the olive oil, and grated garlic. Using quick bursts, whiz until just starting to come together, scraping down the sides frequently.
4. Season with salt, plenty of freshly-cracked black pepper, and a spritz of lemon juice. Add the grated parmesan and whiz until just combined, pouring the remaining oil into the blender in a steady stream with the motor running. Add the remaining pine nuts and whiz briefly to retain some texture.
5. Taste and season the pesto, adding a little more lemon, salt or parmesan to balance out the flavors. You should have a loose, fragrant pesto sauce that spoons easily - add a splash of water if needed.
6. Meanwhile, carefully take the tomatoes out from under the broiler. You’ll notice they will have released a fair bit of juice, but don’t panic - this cooks down into a sweet and tangy sauce with the balsamic. Using a spoon, baste tomatoes with the vinegar and return to the broiler under high heat.
7. Continue checking and basting the tomatoes until liquid reduces by half and the skins are starting to blister in places, around 20 minutes. Allow to cool before serving, any excess liquid will thicken upon standing.
8. Next, prepare pasta as directed, saving 1 cup of the cooking water before draining.
9. Once the pasta is cooked, drain and return it to the warm pot, off the stove. Working quickly, stir through about 1 cup of the basil pesto with ¼ cup of the starchy cooking water. Continue stirring until the residual heat from the pasta melts the cheese, adding more dollops of pesto and pasta cooking water until the penne is glistening and evenly coated.
10. To serve, grate over some extra parmesan and scatter with remaining pine nuts for crunch. Spoon over the roasted tomatoes and their delicious balsamic sauce, and enjoy at once.