Cream the butter well in a mixer with a paddle attachment. Add the sugars and continue to mix well. Add the egg and vanilla and mix well. Sift the flour with the baking soda and the salt then add it to the mixer and blend. Add the peanut butter and mix well. Roll into 1/2-inch balls and place on a greased sheet pan 1-inch apart. Press a fork down on the surface lengthwise then crosswise to make a grid pattern. Bake for 5 to 8 minutes at 400 degrees until light golden brown. Let cool on the pan.
Place a small scoop of grape jelly ice cream on the bottom (flat) side of a cookie and top with another cookie to make a sandwich. Place in the freezer and repeat with the remaining cookies.
Grape Jelly Ice Cream:
Fold grape jelly into vanilla ice cream, leaving some streaks of jelly. Freeze until ready to use in the sandwiches.