In 2-quart saucepan, heat oil over medium heat. Add mushrooms and garlic; cook 3 to 5 minutes, stirring frequently, until tender. Remove from saucepan; place on plate and cover to keep warm.
In same saucepan, heat 1/3 cup water to boiling. Add sugar snap peas; return to boiling. Stir; reduce heat to low. Cover; simmer 3 to 5 minutes or until peas are crisp-tender. Drain; return peas to saucepan.
Return mushrooms with garlic to saucepan; stir in tomatoes and basil. Spoon into serving bowl; sprinkle with cheese.