Preheat oven to 375 degrees.

In a medium bowl, mix together the graham cracker crumbs, butter and 4 Tbsp of the sugar. Press the mixture onto the bottom and up the sides of a 9" tart pan with a removable bottom. Bake for 8 minutes. Remove to a rack to cool completely.

Spread the ice cream into the cooled tart shell. Smooth top. Freeze completely, 4 hours or overnight.

Core and slice the apples. Place them in a bowl and toss with the remaining 2 Tbsp sugar. Set a large nonstick skillet over medium-high heat; add the apple slices and cook until light golden brown yet still tender-crisp, about 3 minutes, turning once. Allow the apple slices to cool. To assemble the tart, arrange the apple slices over the ice cream in concentric circles, overlapping slightly. Garnish with mint sprig. Cut into wedges to serve.