There are some restaurants in the Brian Head area. And a small grocery, called Apple Annies, down on state route 143 just as you enter the Brian Head area as you come up the mountain. There's also a General Store that has stuff in the main Brian Head mall, just next to the main ski slope. Have a great time with your gastronomical exploring.
But don't expect a lot in this department. You might want to consider purchasing some supplies in Cedar City, exit 57 on Interstate 15 before going up the mountain. There's a Wal Mart just to the west of that exit, and a Smith's Food King just to the north.
In Parowan, there is a small grocery store with limited hours, but reasonable prices and a good selection.
Restaurant wise in Brian Head, there are some pizza places, a Mexican place (just below the house), and some good eating in the local hotels, such as Cedar Breaks and the Doubletree Resort and Spa by Hilton.
If you're willing to spend a half hour driving, Cedar City has a few restaurants, some local chains, and some independent restaurants (sushi, Thai, Mexican, American diner).
We usually cook. Nuff said.
Oh, and one more thing. You might find food in the cabinets, and, possibly, in the refrigerator. Our cleaning staff usually throws out the perishables, but sometimes our cleaning staff are guys, and we're not sure they know what a perishable is. So, if you find anything in the cabinets or the refrigerator that appears safe, you're free to use it. Or, feel free to throw it out. Entirely up to you. Please use caution and common sense when using anything that you find food stuff wise in the kitchen; obviously, because of the transient nature of the people who come in and out of the place, we can't guarantee the quality or safety of food stuffs found within. We do try to keep various types of spices and the like in the far left upper cabinet. You might find some canned food, which, unless someone is really devious, should be safe to consume.
The antacids are mine; hey, my wife is Filipino, and her cooking, oh, enough said.