Preheat oven to 350 degrees F. In a blender or food processor, combine tofu and eggs. Cover and blend or process just until combined. Transfer to a large bowl; stir in soy cheese, 1 tablespoon of the basil, the pepper, and salt. Set aside.
In a large skillet, heat olive oil over medium-high heat. Add mushrooms, asparagus, and shallots. Cook and stir for 5 to 8 minutes or just until tender; cool slightly. Stir vegetable mixture into tofu mixture, stirring until well mixed.
Divide mixture among six 6-ounce ramekins or au gratin dishes. Place filled ramekins in a 15x10x1-inch baking pan.
Bake, uncovered, about 20 minutes or until set and edges are bubbly. Sprinkle with the remaining 1 tablespoon basil. Serve warm.