Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Line a baking sheet with aluminum foil.
Place toast on prepared baking sheet and drizzle each side with about 1 teaspoon olive oil.
Stir goat cheese, thyme, pepper together in a bowl until soft and spreadable.
Spread cheese mixture on each piece of toast all the way to the edges so entire piece is covered.
Top each toast with 3 peach slices; drizzle remaining olive oil and sprinkle salt over the top.
Broil in the preheated oven until tops and edges are lightly browned and cheese and peaches are warmed through, about 2 minutes.
