Preheat oven to 350 degrees F. Butter an 8-inch springform pan.

In a medium bowl, stir together crumbs, butter, sugar, stevia, and cinnamon until combined. Reserve 1/2 cup of crumb mixture. Press remaining mixture firmly and evenly over the bottom and up the sides of prepared pan.

Scatter reserved crumbs onto a small baking sheet. Bake crust and crumbs on baking sheet until crust is set and crumbs are browned, about 15 minutes. Let cool completely.

In a large bowl or the bowl of a stand mixer fitted with the paddle attachment, beat cream cheese until very smooth. Scrape down sides of bowl and add brown sugar, stevia, cinnamon, cloves, ginger, and nutmeg. Beat, scraping down sides of bowl, until smooth and combined. Beat in eggs one at a time, scraping sides of bowl after each addition. Add pumpkin and beat just until smooth and homogenous.

Scrape mixture onto the baked crust, smooth top, and set pan on a baking sheet. Bake 30 minutes, then reduce oven temperature to 325 degrees F and bake until the edges of the cheesecake are puffed but the center still looks moist and jiggles when pan is tapped, 15 to 20 minutes more.

Transfer cheesecake to a rack to cool completely, at least 40 minutes. Refrigerate until cold, at least 6 hours or up to 24.

Beat yogurt, stevia, and vanilla together in a medium bowl until smooth. Spread over chilled cheesecake. Sprinkle reserved toasted gingersnap crumbs on top of cheesecake and serve.