Slice the cleaned sprouts down the middle, vertically. Chop the shallots and garlic up fine.
Preheat your grill to medium high.
Once the grill is all set, carefully set the a griddle or a larger frying pan on the grill. Put the butter into the pan to melt. Do not let the butter start to burn. Place the sprouts, cut side down, in a single layer once the butter is completely melted. Then add the shallots and garlic over top.
When they are starting to caramelize it is time to turn the sprouts over, sprinkle with salt and pepper to taste and allow them to cook for another 5 minutes.
Add the enough stock to cover the bottom of the pan and up the sides of the sprouts a little, like 1/8-inch maximum, close the grill lid and let them simmer in the stock until the liquid is gone. They should be tender-crisp.
Serve these hot with more salt and pepper, gravy or a little sprinkling of parmesan cheese.