In a microwave-safe bowl combine almond extract, butter, and brown sugar. Microwave on high 1 minute; stir and microwave an additional 1 minute until bubbly.
Spray a bundt pan with nonstick cooking spray. Place frozen dinner rolls in prepared bundt pan. Pour sugar mixture over rolls; sprinkle with almonds and vanilla pudding mix. Cover and let rise overnight.
Preheat oven to 350 degrees. Bake 25-30 minutes until golden brown. Remove from oven and let cool 10 minutes. Invert bread onto a plate sprayed with non-stick cooking spray. Serve warm.