Combine first 6 ingredients in a bowl, stirring well. Add shrimp to bowl; toss to coat. Let stand for 5 minutes. Remove shrimp with a slotted spoon, and reserve marinade. Combine broth and cornstarch in a small bowl, stirring with a whisk.
Heat oil in a large nonstick skillet over medium-high heat. Add shrimp to pan; sauté 3 minutes or until done. Remove shrimp from pan. Add reserved marinade to pan; cook 1 minute or until slightly thick. Add broth mixture to pan; bring to a boil. Add spinach to pan; cook 1 minute or until spinach wilts. Serve with shrimp.