Make toast. Set the rack in the oven to the middle position, and turn on the oven itself with the grill function to the maximum temperature for preheating. Put the slices of bread on a baking sheet, brush with butter, and place the baking sheet under the grill. Fry the bread until golden brown, about 1-2 minutes on each side. Cut the crust off the hot toast. Cut each cooled fried slice into 4 pieces.
Prepare a topping for a snack with olives. Remove the zest from the lemon half on a fine grater. Place the olives, rosemary, garlic, and zest into the bowl of the kitchen processor. Pulse and gradually add olive oil until smooth. Transfer the paste to a bowl, add about 1 teaspoon of lemon juice, salt, and pepper to taste. Cut hot pepper into thin strips.