Brush a 20 cm / 8-inch square baking dish with 1 tsp olive oil. Bring the water and 1 1/4 tsp salt to a boil in a 3-quart / 2.8 L heavy saucepan, then pour in the polenta in a thin stream while whisking constantly.

Reduce the heat to low and cook for 25 minutes, stirring with a wooden spoon every 3 to 4 minutes, until the polenta is thick, pulls away from the sides of the pan and tastes tender with no grit. Stir in 1 tbsp olive oil, the nutritional yeast and 1/4 tsp pepper.

Scrape the polenta into the dish and smooth it to an even 2.5 cm / 1-inch layer. Cool uncovered for 15 minutes, then refrigerate until cold and fully firm, at least 2 hours in total. If holding it longer, cover it once cold and keep it up to 3 days.

Heat the oven to 220 C / 425 F with racks in the upper and lower thirds. Cut the eggplant, zucchini, peppers and onion. On a 33 x 46 cm / 13 x 18-inch sheet pan, whisk the tomato paste with 3 tbsp olive oil, the thyme, 3/4 tsp salt and 1/2 tsp pepper, then toss in the vegetables and garlic. Spread everything in a single layer and keep the cherry tomatoes aside.

Turn the cold polenta out onto a cutting board and cut it into 8 rectangles, about 10 x 5 cm / 4 x 2 inches. Brush a second 33 x 46 cm / 13 x 18-inch sheet pan with 1 tbsp olive oil, arrange the pieces with space between them, and brush the tops with the remaining 1 tbsp oil.

Roast the vegetables on the upper rack and the polenta on the lower rack for 20 minutes. Pull both pans out, flip the polenta with a thin metal spatula once the bottoms release easily, stir the vegetables and scatter the cherry tomatoes over them.

Roast for 15 minutes more, until the polenta is deep golden with crisp edges and the vegetables are browned at the edges and tender when pierced. Mash the roasted garlic into the vegetables, then toss with the vinegar and basil. Taste, add a pinch of salt if needed, and serve over two polenta rectangles per plate within 10 minutes.