Preheat the oven to 300 degrees F (150 degrees C). Lightly butter a 10-inch springform pan.

Place sandwich cookies in a resealable plastic bag; crush with a rolling pin. Pour crumbs into a bowl. Add scraped seeds of 1 vanilla bean; stir to combine. Drizzle crumbs with melted butter; stir to combine. Press into the bottom and up sides of the prepared pan; set aside.

Beat softened cream cheese and sugar in the bowl of a stand mixer fitted with the paddle attachment on medium speed until smooth, about 3 minutes. Beat in eggs one at a time, beating well after each addition before adding the next. Add sour cream, heavy cream, remaining scraped seeds of 2 vanilla beans, and vanilla extract; beat on medium-high speed until blended and smooth, about 1 minute.

Pour cream cheese mixture into crust, leaving about 2 inches of space from the top of pan for cake to expand as it bakes.

Place a baking dish onto the bottom rack of the preheated oven; fill halfway with boiling water. Place cheesecake on middle rack, above dish of boiling water; bake until a small knife inserted into the center comes out clean, about 1 hour and 20 minutes.

Turn the oven off; let cheesecake cool inside the oven for 1 hour. Cover the cheesecake with plastic wrap, then aluminum foil, and refrigerate at least 4 hours or overnight before serving.