Using a hand mixer, whip heavy cream into stiff peaks on medium-high speed, about 4–5 minutes. Set aside.
In a separate container, beat cream cheese and granulated sugar together on medium speed until smooth and creamy. Scrape down sides and bottom of bowl with rubber spatula as needed.
Add confectioners’ sugar, sour cream, lemon juice, and vanilla extract. Beat 2–3 minutes until smooth and creamy.
Using a rubber spatula, fold whipped cream into cheesecake filling until combined.
Put cheesecake filling into a piping bag. Place some crumble in bottoms of cones, pipe in cheesecake filling, and add fresh strawberry chunks and a few sprinkles of crunch mix. Drizzle with melted chocolate, if desired. Refrigerate leftovers.