Preheat your oven to 325°F (160°C). Spray a mini tart pan, or alternatively four 4-inch tart shells, with oil to prevent sticking, and set aside. Preparing your equipment first makes assembling the recipe much smoother.
In a mixing bowl, beat the vegan butter using a hand mixer or stand mixer until it is light and fluffy, about 3-5 minutes. Scrape down the sides if necessary. Add 1/4 cup powdered sugar and beat again for another 2-3 minutes until the mixture is well blended. Scrape the sides and add the all-purpose flour and lemon zest. Mix on low speed, just until everything comes together—do not over-mix to keep the crust tender.
Divide about 2 tablespoons of the prepared dough (from Step 2) into each tart mold. Press evenly into the sides and bottom, aiming for a thickness between 1/8 to 1/4 inch. If using 4-inch tart shells, roll out the dough on a floured surface to the same thickness and cut circles just larger than your molds. Gently fit the dough inside each greased tart pan, pressing lightly to fill. Prick the bottoms with a fork and place the molds in the freezer for at least 15 minutes while making your filling. Chilling prevents the crust from shrinking while baking.
Scoop out just the solid portion from the top of the chilled can of coconut milk into a medium mixing bowl. Add the vegan cream cheese, 1/3 cup powdered sugar, and vanilla extract. Blend everything together with a hand mixer until the mixture is completely smooth. Cover and refrigerate until you are ready to fill the tart shells. I like to chill the filling to help it thicken up and set nicely in the tarts.
Remove the tart molds with the chilled dough (from Step 3) from the freezer and bake them in the preheated oven for 15-20 minutes, or until the edges begin to turn golden. Take the shells out and let them cool in the pan for 3-5 minutes before transferring them to a wire rack to cool completely.
Once the tart shells are completely cool, scoop or pipe the chilled cream cheese filling (from Step 4) into the shells until they are about 2/3 full, spreading evenly. Finish each tart by topping with a generous handful of assorted fresh berries. Serve immediately or refrigerate until ready. For extra flavor, I sometimes add a touch more lemon zest over the top just before serving.