- 1 cup plus 3 tablespoons corn oil
- 2 tablespoons white balsamic vinegar
- 5 teaspoons chopped fresh thyme
- 4 teaspoons chopped fresh oregano
- 8 5-inch diameter portobello mushrooms
- 1 pound assorted fresh wild mushrooms (such as oyster and stemmed shiitake), sliced
- 1 1/2 cups fresh corn kernels
- 1 cup crumbled Cotija or feta cheese
Whisk 1 cup oil, garlic, vinegar, 3 teaspoons thyme, and 2 teaspoons oregano in medium bowl to blend. Season generously with salt and pepper. Transfer 1/3 cup garlic-herb oil to small bowl; reserve.
Trim and thinly slice portobello stems; set aside. Brush both sides of portobello caps with remaining garlic-herb oil; place caps, rounded side down, on large rimmed baking sheet.
Preheat broiler. Broil portobello caps until tender, about 5 minutes per side. Remove from broiler. Turn caps rounded side down. Heat 3 tablespoons oil in heavy large skillet over medium-high heat. Add assorted mushrooms and portobello stems; sauté 5 minutes. Stir in reserved 1/3 cup garlic-herb oil; sauté until mushrooms are tender, about 5 minutes. Add corn; sauté until tender, about 3 minutes. Add cream; simmer until almost absorbed, about 2 minutes. Stir in cheese. Season with salt and pepper. Divide mixture among portobello caps, mounding in center. DO AHEAD: Can be made 6 hours ahead. Cover; chill.
Preheat broiler. Broil portobellos until heated through, about 5 minutes. Sprinkle with 2 teaspoons each thyme and oregano.