Grate the dill Havarti cheese until you have a heaping mound, about 1½ cup. Chop or slice your pickles until you have about ¼ cup.
Heat the butter in the skillet until it is melted.
Add one flour tortilla. On one side of the tortilla, sprinkle half your cheese mixture. Top with pickles.
Fold the empty side of the tortilla over the dill Havarti cheese and pickles, essentially folding it in half.
Fry the dill Havarti quesadilla until the bottom is golden brown, about 2 to 3 minutes. Then, flip it over and brown the other side, about another 2 to 3 minutes.
Transfer to a plate and garnish with sprigs of dill.