Preheat oven to 350°.
Heat oil in a large nonstick skillet over medium-high heat. Add the cabbage and next 5 ingredients (cabbage through garlic); sauté 3 minutes or until the cabbage is crisp-tender. Remove from heat; stir in potato, peas, and soy sauce.
Place 4 tortillas on a large baking sheet. Spread about 1/2 cup potato mixture over each tortilla; top each with 1/4 cup cheese and a tortilla. Bake at 350° for 15 minutes or until thoroughly heated. Cut each quesadilla into 4 wedges.