In a small saucepan, warm vegetable stock over low heat.
Heat olive oil in a Dutch oven or heavy bottomed pot over medium heat.
Add the onion and cook until translucent. Add the garlic, stir to combine. Add the carrots and cook for about 1 minute more.
Add the brown rice and stir to coat. Allow to cook (toast) for about 2-3 minutes, stirring frequently. Add the wine and cook until evaporated, stirring often.
Add one cup of the vegetable stock and cook until absorbed. Continue adding one cup at a time, stirring often, allowing stock to be absorbed each time until rice is just tender and mixture is creamy (this will take 6-7 cups of stock). Stir in peas towards the end of cooking so that they may warm.
Season with salt and pepper to taste. Serve immediately.