Place kimchi, onion, ginger, and sugar in a food processor and blend until smooth.
Melt 3 tbsp butter in a large skillet over medium heat. Add kimchi puree, and sauté until fragrant, about 1 min. Add rice, stir to combine, and continue to sauté for another 1-2 min.
Add wine and soy sauce, Stir to combine and leave on low heat. When all the liquid has been absorbed by rice, start adding 1 cup of broth to the pan at once. Let the rice fully absorb the broth before adding the next cup. Continue this process until the rice is tender. Season to taste.
Melt remaining 3 tbsp butter in another skillet over medium heat. Add shrimp and sauté until just about cooked through, about 2 min per side. Add garlic, stir to combine, and continue to cook for 2-3 minutes. Remove skillet from the heat and add chives and cilantro, stirring to coat the shrimp. Season to taste with salt and pepper.
Divide risotto between bowls and top with garlic shrimp.