Preheat the oven to 325°F. Line a 12-cup muffin pan with cupcake liners.
In a medium bowl, stir together the graham crackers and melted butter until well-combined.
Evenly divide the graham cracker mixture among the muffin cups, pressing it firmly into the bottoms of the cups. (A small dry measuring cup or the bottom of a shot glass work best for this.)
Bake the cups for 5 minutes then remove them from the oven and let them cool while you prepare the filling.
Add the cottage cheese to the bowl of a food processor and process until it is smooth and creamy. Transfer the cottage cheese to a medium bowl then add the cream cheese, sugar, lemon zest, lemon juice and vanilla extract. Using a handheld mixer, beat the ingredients until combined then add the eggs one at a time, between each addition. (Alternately, combine the ingredients in a stand mixer fitted with the paddle attachment.)
Divide the cheesecake mixture evenly among the muffin cups. (It should be to the top of each wrapper.)
Bake the mini cheesecakes until they are just set in the centers, 20 to 23 minutes.
Remove the mini cheesecakes from the oven and let them cool completely in the pan. Transfer the mini cheesecakes to a baking sheet and refrigerate them for a minimum of 3 hours and up to overnight before serving.