Heat oven to 350F. Prepare sheet pan with parchment paper. Melt butter and set aside. In food processor, pulse graham crackers and sugar until crumbs. Slowly drizzle in the melted butter and pulse until is thoroughly mixed.
Pour mixture onto sheet tray and use the back of a large measuring cup to flatten into a rectangular shape. Bake for 8 minutes, or right before edges start to brown. Cool and cut or break into bite-sized pieces and set aside.
No-Churn Cheesecake Ice Cream
In a large bowl using a hand blender, or in bowl of stand mixer, beat cream cheese and sugar until fluffy. Add in sweetened condensed milk and vanilla bean paste, and mix to combine.
In separate bowl, whip heavy cream to stiff peaks. Fold into cream cheese mixture 1/3 at a time.
Add 2/3 of the graham cracker crust pieces and fold into ice cream. Pour half of ice cream into standard loaf pan. Sprinkle half of remaining crust onto ice cream. Add remaining ice cream, then remaining crust pieces. Freeze for 24 hours (cover with plastic wrap or parchment after 4 hours).