In a medium-sized Dutch oven, heat olive oil over medium heat. Add sliced shallots to pot and stir to coat with oil.
Let them cook for 8 - 10 minutes until they begin to caramelize. (Reduce heat if they are browning too quickly.)
Add wine and reduce by half. (This should take 4 - 5 minutes.)
Next, add the mushrooms to the shallots. Season with salt and pepper, stir to combine and add the sprig of rosemary. (Mushrooms will release a lot of liquid, it will take 20 - 25 minutes for them to cook down.) Stir mushrooms occasionally to prevent burning and scrape the bottom of the pot to get all the yummy brown bits that have stuck as it is cooking.
Add the fregula and garlic, stir it to combine, then add the stock. Add the cheese rind if you have one.
Bring to a boil over medium high heat, then cover and reduce heat to medium/medium low. Simmer for 10 - 12 minutes.
Remove lid and continue to cook for an additional 2 - 4 minutes, until fregola has thickened slightly.
Turn off the heat. Add all but 2 tablespoons of the chopped parsley to the fregula. Stir to combine. Serve with extra grated parmesan and the remaining parsley on top.