Preheat the oven to 350°F (175°C).
In a medium saucepan, combine cranberries, sugar, and water. Cook over medium heat until cranberries pop and soften.
Blend the cranberry mixture until smooth, then strain through a fine sieve to remove solids.
Return the mixture to the pan, whisk in cornstarch, and cook over medium heat until thickened.
Remove from heat and whisk in eggs, one at a time, until fully incorporated.
Add butter pieces and stir until melted and smooth.
Pour the curd into the tart crust and smooth the top.
Bake for 18-20 minutes until the curd is just set.
Let cool completely before serving. Store in the refrigerator.