Add 6 cups water and a few thyme and fresh oregano sprigs. Simmer, covered, for one hour, covered. Use a slotted spoon and strain out the solids.

Halve the tomatoes and cut the remaining vegetables as indicated in ingredients list. Halve the mushroom caps if large. Cut the onions in quarters.

Gently toss all the vegetables, garlic halves and mushrooms with about half a cup of the olive oil, sea salt, and pepper in a large mixing bowl.

Heat a grill pan or stove top griddle over medium flame, lightly oil it and place the vegetables and mushrooms in the pan, in batches if necessary, until al dente, tender enough to eat and slightly and pleasantly charred.

Add enough water to the mushroom liquid to suffice for boiling the pasta. Bring the liquid to a boil, season it with salt, and boil the pasta.

Drain the pasta, reserving a cup of the boiling liquid. Remove the vegetables from the griddle as they are ready, nicely charred and tender. Toss with the pasta and vegetables all together. Open and squeeze out the garlic pulp. Drizzle in additional olive oil, the balsamic vinegar, basil leaves and a little of the mushroom cooking liquid. Adjust seasoning with salt and pepper as desired, and serve.