Combine crumbs and melted butter. Pat evenly over bottom and about 3/4 inch up the side of a removable-rim 8-inch cheesecake or cake pan (at least 13/4 in. deep).
In a food processor or bowl, whirl or beat cream cheese, milk, egg whites, and vanilla until very smooth. Stir in 1/4 cup chocolate chips.
Scrape batter into prepared pan. Evenly sprinkle batter with remaining chocolate chips.
Bake in a 350° oven until cake jiggles only slightly in the center when gently shaken, about 30 minutes.
Run a thin-bladed knife between cake and pan rim. Refrigerate cake, uncovered, until cool, at least 21/2 hours. Serve, or if making ahead, wrap airtight when cool and chill up to 2 days. Remove pan rim and cut cake into wedges.