A sparkling rose will bring out all the high points of these savory cakes.
Heat chicken stock and keep warm. Heat oil and 1/2 tablespoon butter in a small pan over medium heat. Add onion; saute until fragrant, 2 minutes. Add rice and beets; saute, stirring, 2 minutes. Add wine; stir until almost absorbed. Add stock, 1/2 cup at a time, stirring until almost absorbed between each addition. Cook until rice is al dente, about 17 minutes. Season lightly with salt. Spread mixture on rimmed baking sheet or glass baking dish to cool to room temperature, then stir in cheese and breadcrumbs.
Using a 1 1/4-inch scoop, form rice into balls; flatten. Heat 3 tablespoons butter in a nonstick skillet over medium heat; saute rice balls in batches until golden on both sides. Blot briefly on paper towel; transfer to serving tray. Garnish with chives. Serve immediately.