Use a vegetable peeler to peel away top third of skin on each apple. Use a sharp paring knife or melon baller to remove core of each apple, leaving bottom end intact. Scrape away any remaining bits of core and seeds.
Combine walnuts, sugar and butter in a small bowl and mash with a fork until mixture comes together in coarse crumbs. Tightly pack apples with mixture.
Arrange apples in a microwave-safe baking dish so they're not touching each other. Drape with plastic wrap and microwave until apples are soft when pierced with a skewer, 5 to 7 minutes (depending on power of your microwave). Carefully remove plastic (there will be steam) and let stand to cool for 10 minutes.
Place each apple in a dessert bowl along with a scoop of ice cream. Drizzle juices from baking dish over apples, if desired. Serve immediately.