Pour the broth in a saucepan, cover and set over medium-high heat. Bring to a solid simmer and keep it that way.
In a 10? skillet, put 2 T of butter. Melt and then brown it. When brown, put a third or so of your mushrooms. Don’t crowd them; in fact, don’t let them touch. When they’re golden and just cooked through, about 2-3 minutes (flip during that time), remove them with tongs or a slotted spoon to a plate. Repeat with the remaining mushrooms (you shouldn't need to add more butter). When the mushrooms are done, set them aside.
In the same skillet (don’t wipe it out), pour 2 T of olive oil. Because the skillet is already warm, it should heat up quickly. Add the shallots, marjoram and mint, stir to combine, and remove the skillet from heat. Set aside.
In a 4 quart saucepan, add the remaining 1 T of butter and 1 tsp of olive oil. Heat over medium-high until the butter is melted. Add the rice and stir to combine. Cook 2-3 minutes, until the rice is nice and toasty. Add the salt and white wine and stir.
When the wine looks to be almost totally gone, add the broth, ½ c at a time, stirring fairly continuously and adding the next ½ c only when there looks to be just a tiny bit of liquid remaining in the rice. After you’ve added 2 c of broth, stir in the shallot-herb mixture. Continue adding the broth. When you have added 4½ cups of broth, stir in 2/3 of your browned mushrooms, reserving the remaining third for garnishing the finished risotto. After you've added 5 cups of broth total, check the doneness of the rice. If it’s still too al dente for you, add another ½ c of broth and then check again.
When it’s done to your liking, stir in the goat cheese until it’s well-incorporated. Spoon risotto into bowls, and top with remaining mushrooms and a sprig of marjoram if you want.