To prepare potato cakes, heat oil in a large nonstick skillet over medium-high heat. Add 1/4 cup onion, chile, and garlic; sauté 3 minutes. Combine onion mixture, milk, salt, beans, and egg white in a food processor; process until smooth, scraping sides of bowl once. Stir in potato.
Place skillet coated with cooking spray over medium-high heat until hot. Spoon 1 tablespoon potato mixture per cake into pan, spreading each to form a 2-inch circle; cook 2 minutes or until lightly browned. Carefully turn cake over; cook 2 minutes on other side. Repeat procedure with the remaining potato mixture. Keep cakes warm.
To prepare dressing, combine pineapple juice and next 4 ingredients (pineapple juice through lime juice) in a saucepan; bring to a boil. Reduce heat; simmer 5 minutes. Stir in pecans and bacon.
Arrange 1 cup salad greens on each of 6 plates. Arrange 4 potato cakes around greens. Drizzle 1/4 cup warm dressing over each serving.