Combine brown sugar and cardamom thoroughly. Set bananas on a large plate, cut side up. Sprinkle sugar-cardamom mixture over bananas, pressing down gently to help mixture adhere.

Choose a skillet large enough to accommodate all banana pieces and place it over high heat. Add butter and swirl to coat pan. Add bananas, cut side down, and cook for 1 minute. While bananas are cooking, sprinkle with any remaining sugar-cardamom mixture. Turn bananas over and cook for 15 seconds more. Remove from skillet and divide among plates, with the browned cut sides up.

Pour juice into skillet; stir for about 10 seconds to collect any browned bits. Immediately pour over bananas and serve.