Cranberry Sauce: In a small saucepan, bring cranberries, sugar, water, and lemon juice to a slow simmer over medium heat. Simmer for 7-8 minutes, crushing cranberries with a spoon as they begin to pop. Remove from heat and set aside to cool. Once cool, push through a mesh sieve to remove skins.
Crust: In a food processor, blend together shortbread cookies and pistachios until a sand-like mixture forms. Add butter and mix thoroughly.
Cheesecake: Using an electric mixer, whip together cream cheese, sugar, and vanilla until combined, light, and fluffy. Add eggs one at a time, slowly mixing in between each addition until just incorporated.
Preheat oven to 325°F. Assemble cheesecakes by placing approximately 1 Tablespoon shortbread and pistachio crust into the bottom of each mini cheesecake tin. Tamper down until a uniform crust forms. Add cheesecake filling to the top of each tin. Add ¼ teaspoon of cranberry sauce to the top of each cheesecake and swirl around with a toothpick.
Bake cheesecakes for 18-20 minutes until set around the edges; the centers may still jiggle and that's ok. Let cool at room temperature for 45 minutes to an hour. Chill in the fridge for 1-2 hours. The cheesecakes will set up in the fridge and be much easier to remove from the mini cheesecake pan after chilling.