Combine crumbs and melted butter. Pat evenly over bottom and about 1/2 inch up the side of a removable-rim 9-inch cheesecake or cake pan (at least 1 3/4 in. deep).
Bake in a 350° oven until crust is slightly browner, 10 to 12 minutes.
Meanwhile, in a large bowl, use a fork to blend eggs, 1 cup sugar, 3 cups cheese, and vanilla until well mixed. Scrape mixture into hot or cool crust.
Bake in a 350° oven just until center jiggles only slightly when cake is gently shaken, 40 to 45 minutes.
Meanwhile, stir remaining cheese with remaining sugar until smooth. Spoon onto cake and gently spread to cover top.
Return to oven and bake to firm topping slightly, about 10 minutes. Run a thin-bladed knife between cake and pan rim. Refrigerate cake, uncovered, until cool, at least 2 hours.
Serve, or if making ahead, wrap airtight and chill up to 1 day. Remove pan rim and garnish cake with berries; cut into wedges.
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