To roast peppers, set broiler to high. Line a baking tray with parchment paper. Slice peppers lengthwise into large pieces around the stem and core. Remove seeds. Place pepper pieces skin-side up and place in broiler for about 8 to 10 minutes or until the skin has turned most black. Remove tray from oven and place peppers in a bowl. Cover with foil or plastic wrap and let cool. The steam helps the skins to separate from the flesh. When peppers are cool, peel blackened skins and discard them.
Add the garlic to the food processor and pulse to mince. Add the roasted red peppers, feta cheese, olive oil, lemon juice, oregano, red pepper flakes and cayenne. Pulse a handful of times to get desired texture. Taste and adjust any seasonings as need. Add salt to taste, if necessary.