In a mixer, put butter and mayonnaise and bear with paddle attachment until well mixed. Be sure to scrape down the sides of the bowl to incorporate all butter as it may stick to the bowl. Generously butter one side of each slice of bread with the butter/mayo mixture. Be sure to butter to the very edges. On the unbuttered side, crumble approximately 2 ounces of goat cheese.
Top cheese with several slices of fresh peaches. Top with two oz. of crumbled cheese and finally, the buttered bread, butter side out.
Heat griddle to about 350°F. Place all sandwiches on griddle and allow to cook slowly. If your heat is too high it will burn the bread and the inside will not be hot.
Once golden brown, gently flip and repeat until cheese is melted and hot. If the bread browns prior to the inside being hot, place pan with sandwiches in oven at 450°F to allow to finish.
Simply put 1/2 tablespoon of the same filling at the end of an endive leaf and serve.