Microwave frozen potatoes as directed on box. In food processor, place cooked potatoes and beans; process about 30 seconds or until almost smooth. Place mixture in medium bowl. Stir in onion and chiles.
Heat 12-inch nonstick skillet over medium heat. On half of each tortilla, spread 1/3 cup potato mixture. Sprinkle with 1/4 cup of each of the cheeses. Fold each tortilla over; press to flatten slightly.
Cook 2 or 3 quesadillas, with potato mixture on bottom, in hot skillet for 1 to 2 minutes on each side until tortillas are golden brown. Remove from skillet; cool slightly. Repeat with remaining quesadillas.
With pizza cutter, cut each quesadilla in half. Serve warm with salsa or sour cream.