In a medium saucepan, bring the stock to a boil over medium-high heat. Add the beans. Reduce the heat to low, and simmer until the beans are tender, about 5 to 8 minutes. Drain the beans and reserve 1 cup of stock. Place the drained beans and reserved stock in a blender or food processor. Add the mint and blend until smooth. Season with salt and pepper, to taste.
In a large skillet, heat enough oil to fill the pan 1/4-inch deep, over medium-high heat. Season the fish with salt and pepper on both sides. Cook for 3 to 4 minutes each side until brown and the center is just opaque.
Divide the fava bean puree between 4 serving plates. Place a filet of red snapper on top of the puree. Serve immediately.