Preheat the oven to 400°F.

Brush any dirt from the outside of the mushrooms and using a teaspoon, carefully scrape the gills from inside the cap and discard. Arrange the mushrooms in a single layer on a nonstick baking sheet.

Whisk together 1 tablespoon of the olive oil and 2 teaspoons of the balsamic vinegar in a small bowl. Brush the mushrooms with the mixture, season with salt and pepper and roast them just until tender when pierced with the tip of a knife, about 5 to 7 minutes. Remove from the oven and blot any accumulated liquid from inside the mushroom caps with a paper towel. Set aside

While the mushrooms roast, heat the remaining 2 tablespoons of olive oil in a heavy skillet over medium heat. Add the onion and sauté until softened, 2 minutes. Add the garlic and cook until fragrant, 1 minute additional. Add the sausage and continue cooking, until the sausage is browned and cooked through, 4 to 5 minutes longer. Add the remaining balsamic vinegar, sun-dried tomatoes, provolone cheese and basil. Combine well and season to taste with salt and pepper.

Divide the sausage mixture between the 4 mushrooms caps, pressing the mixture gently with a spoon to form a mound. Return the mushrooms to the oven for 5 to 7 minutes, until the cheese is melted throughout.