In a food processor, pulse the sun-dried tomatoes with the garlic and cayenne until finely chopped, then puree until smooth. Add the mayonnaise and pulse just until blended.
Make Ahead: The aioli can be refrigerated for up to 1 week. Let return to room temperature before serving.
Serve With: Grilled beef, lamb or chicken or on grilled vegetable or crab-cake sandwiches.