Pre-heat the oven to 375 degrees F.
Sauté the diced onions and in the olive oil and ½ tsp of salt, over medium heat in a medium sized enameled Dutch oven. The correct amount of oil will make the onions uniformly glisten, but not pool in the pan. Sauté until the onions are translucent. Try to minimize any browning of the onions. Expect 4-5 minutes
Add the minced garlic to the pot. You do not want the garlic to brown. Stir and sauté for about one minute.
Add the brown rice to the pot and stir to coat each grain with the aromatic infused oil.
Add the splash of wine to deglaze any fond that has developed and stir until the wine has mostly been absorbed by the rice.
Add 4 cups of stock and increase the heat to high to bring the pot to a full boil. As things are heating, taste test for seasoning. It probably needs some some salt at this point, but how much depends on the how salty your selected broth is. At this point the broth should be well-seasoned.
Once a full boil is reached, cover the pot and transfer to the center rack of the 375 degree oven. Also place the baking sheet with the carrots on the top rack. Set a timer for 40 minutes.
While the risotto is cooking in the oven, prepare the fava beans, snap peas and mint.
For the fava beans: They will need to be blanched after they are removed from their pods. Put a few cups of water in a small pot on the stove to bring to a boil. Also, prepare an ice bath by putting ice cubes and water into a medium bowl. Remove the fava beans from their pods. You can "unzip" the pods by pulling on the long fiber that runs from the stem to tip. When all of the beans are removed, blanch them in the boiling water for 1 minute, and then transfer them to the ice bath. Finally, peel the outer skin from the beans.
For the peas: Remove the string from each pod, and cut the pods on a bias into 2-4 pieces depending on the size of the pod.
For the mint: Stack the leaves into a single stack and slice the stack creating julienne cuts.
When the timer expires at 40 minutes, remove the pot from the oven. Remove the lid and stir in the fava beans and snap peas. Recover and return to the oven for 10 more minutes of cooking.
After 50 minutes, remove risotto from the oven. Remove the cover and stir in the butter and the remaining cup of stock. Then stir in the along with the chèvre and the mint.
Finally, plate, add garnishes and accompaniments, and enjoy!