Heat butter in a skillet over medium-low heat; cook and stir pecans in melted butter until toasted and fragrant, 3 to 5 minutes.
Mix pecans, American cheese, sharp Cheddar cheese, extra-sharp Cheddar cheese, mayonnaise, green onions, and cayenne pepper together in a bowl. Press cheese mixture into a tart pan or a spring form pan lined with plastic wrap. Chill in refrigerator for flavors to blend, at least 2 hours.
Spread raspberry preserves over the cheese mixture and allow to sit at room temperature before serving, about 1 hour.