1. Preheat the oven to 425 degrees Fahrenheit. Butter the inside of a 9 1/2-inch tart pan. 

For the Pastry: 

1. In a large bowl, mix the flour, sugar, key lime zest, and cardamom until combined. In a small bowl, beat the egg yolk and vanilla paste until well combined. 
2. Cut the butter into the flour mixture until it makes coarse crumbs. Add the egg mixture and mix until just combined. One tablespoon at a time, add the key lime juice until the dough comes together. It should be crumbly but not dry. 
3. Press the dough to the tart pan until it fills all the nooks and crannies evenly. 
4. Put the tart pan in the freezer until ready to use.

For the Berries: 

1. In a large bowl (I used the same one as I used to make the pastry dough), mix the sugar, flour, key lime zest, and cardamom until combined. Toss in half the blueberries (2 1/2 cups) and mix until well combined. Pour the blueberries and all of the sugar mixture evenly into the tart pan. 
2. Bake at 425 degree Fahrenheit for 15 minutes. Then, turn the oven down to 350 degrees and bake for an additional 35-40 minutes, or until the crust is golden brown. Once during the cooking time, stir the blueberry mixture to make sure that it’s evenly spread out and there is no remaining flour exposed. 
3. Remove from the oven to a wire cooling rack and immediately press the remaining blueberries on top in concentric circles. 
4. Serve warm or at room temperature. Right before serving, dust the tart with confectioners sugar passed through a mesh sieve. Then, add mint sprigs or julienned mint and, if desired, some extra key lime zest. 
5. You can serve the tart as is or with a dollop of ice cream, whipped cream, or crème fraîche.