Melt the butter in a marge heavy bottom pot over medium high heat.
Add the onion and cook for 4-5 minutes until the onion is translucent. Add the garlic and stir to combine. Add the shredded carrots and cook for 1 minute more.
Add the arborio rice and stir to coat the rice with the butter. Cook the rice for about 2 minutes until the outer edges of the rice are translucent and the middle still white. Pour in the white wine and deglaze the bottom of the pan. Cook until the wine has evaporated.
Add 1 cup of the chicken stock and cook until the stock has evaporated. Repeat this step a few times until you've used all of the stock. The rice should look almost like a porridge and have just a slight bit of a bite when tasted.
Add Parmesan cheese, mascarpone cheese and chives and stir to combine. Season with salt and pepper to taste and serve immediately.