Begin by soaking your wood skewers in water for about 10 minutes. Set your grill to medium-high heat and brush the cooking grate with oil to prevent sticking.
Once the skewers are well-soaked with water, place the peach slices and watermelon cubes onto each. In all, you'll need 8 skewers of fruit.
Place the skewered fruit onto the grill. Grill for 3-4 minutes on each side or until grill marks form on the fruit. Remove the skewers of fruit from the grill with tongs.
Add 3-4 scoops of ice cream to a bowl. Top with two grilled fruit skewers. Garnish with a cookie and a sprig of fresh mint.