In a medium saucepan, bring the stock to a simmer. Reduce the heat to low and keep warm.
Meanwhile, in a large, wide pot over medium heat, melt the butter. Add the onion and garlic and sauté until softened and translucent, about 5-8 minutes. Add the rice and cook for a couple minutes. Add the wine and allow it to simmer, while stirring, until it has been absorbed by the rice, and there is no liquid left in the pan. Add 1 – 2 ladles of the warm stock to the pan, and simmer, stirring frequently, until almost completely absorbed. Repeat this process, adding 1 – 2 ladles of stock at a time and stirring frequently, until the rice is cooked, making sure that you wait until the liquid is almost completely absorbed before adding more.
When you add your last bit of stock, also toss in the peas. Continue to stir frequently and after a few minutes, taste the rice to make sure it is cooked but still has a bite to it. Also check the peas are cooked. If you find your rice to be underdone, you can add more stock, again 1 – 2 ladles at a time until it is cooked to your liking. From start to finish, the whole process should take you between 20-25 minutes.
Taste the risotto and add any salt and/or pepper if you would like. Ladle into your serving bowls and garnish each generously with the goat cheese and freshly chopped mint.