Preheat the oven to 350 degrees F (175 degrees C).

Mix cookie crumbs, melted butter, and 2 tablespoons sugar in a medium bowl until well combined. Press mixture into the bottom and 2 inches up the sides of a 9-inch springform pan. Place in the refrigerator for crust to set, about 30 minutes.

Place chocolate chips in the top of a double boiler over simmering water. Stir frequently, scraping down the sides with a rubber spatula to avoid scorching, until chocolate is melted, about 5 minutes. Set aside.

Beat cream cheese and 1 cup sugar in a large bowl until smooth and creamy. Blend in eggs one at a time, mixing after each addition until just incorporated. Gradually pour in melted chocolate, beating on low speed until well blended. Add 1/2 cup sour cream, flour, and vanilla. Blend until smooth, then pour into crust.

Bake in the preheated oven until center is set and filling is firm, 55 to 60 minutes. Turn the oven off. Cool cheesecake in the oven for 1 hour without opening the door. Remove cheesecake to the counter and cool completely at room temperature. Transfer cheesecake to the refrigerator and chill for several hours to overnight.

Stir 1/2 cup sour cream and 1 tablespoon sugar together in a small bowl until well combined. Spread over chilled cheesecake before serving; garnish with chocolate shavings.