Char all of the skin on the peppers. This is easiest to do on a very hot grill, but it can also be done directly over the burner of a gas cooktop or under a broiler.
Move the peppers to an airtight container when they are charred. Let them sit until they are cool enough to handle.
Rub charred skin off of the peppers and discard. Expect to see some dark discoloration under the skin. Also, if a little bit of charred skin remains on the peppers, that is fine. It will lend some more smokey nuances to the finished pesto.
Slice the peppers in half and use the back of a knife to scrape the inside, removing the pith, seeds and stem core.
Use a food processor to make the pesto
Either grate the cheese, or use a knife to dice into small pieces.
Rough chop the garlic cloves.
Place all of the ingredients in the food processor. Run the food processor until the pesto has achieved a pureed consistency.
Notes
I usually use a cheese called Calvander from the Chapel Hill Creamery, which is local to me. Calvander is made in the style of aged Asiago. A nice Parmesan or pecorino Romano would also work nicely.