Combine the garlic, bell pepper, cream cheese, mayonnaise, cayenne, and salt in the bowl of a stand mixer fitted with the paddle attachment. Beat on medium-low speed until well mixed, scraping the bowl occasionally. Add the Cheddar and Monterey Jack, and beat on low speed until the cheese is evenly distributed. Transfer to a serving bowl, cover with plastic wrap, and refrigerate for at least 1 hour and preferably overnight. The garlic will mellow over time and the flavors will meld. Store in an airtight container in the refrigerator for up to 1 week.