In a small dry skillet, toast the chiles over medium-high heat until puffed, approximately 2 minutes. Remove stems and add to a bowl of hot water. Let the chiles soften and soak for 20 minutes; drain.
Add softened chiles, garlic, olive oil, salt, coriander, and cumin to a blender or food processor. Puree until well-combined. Add chile mixture, short ribs and chopped onion to a large bowl. Using your hands, coat the short ribs well in the marinade. Cover with plastic wrap and refrigerate overnight.
Preheat oven to 350 degrees.
In a large, heavy-bottomed, oven safe pot, add shorts ribs and marinade with 2 cups chicken stock. Bring to a boil over high heat. Once boiling, cover and place in the oven. Braise for 2 hours.
Remove from oven, stir in tomato paste, cover and return to the oven. Braise for an additional hour.
When there are 40 minutes left for the short ribs, make the risotto. In a medium saucepan, bring the chicken stock for the risotto to a simmer; cover and keep warm over low heat.
In a large Lagostina skillet, heat olive oil over medium heat. Add the garlic and cook until browned, about 1 minute. Stir in the rice and toast for 2 minutes. Add the wine and simmer until almost evaporated. Pour in approximately 1 cup of the hot stock. Cook, stirring constantly, until the stock has been absorbed. Repeat this process, adding 1 cup of stock at a time and stirring until the rice is tender. You may not need all the stock so test the rice between each addition. It should take approximately 25 to 35 minutes total. Stir in parmesan cheese and butter, and season with salt and pepper. Keep warm over low heat until ready to serve.
Remove ribs using tongs from the pot. Serve short ribs over risotto.