Preheat oven to 350°F (175°C) and line a cupcake tin with paper liners.
In a bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, beat butter and sugar until light and fluffy (about 3-4 minutes).
Add eggs one at a time, beating well after each addition.
Mix in vanilla extract, lime zest, and milk until well combined.
Gradually fold in the dry ingredients, being careful not to overmix.
Gently fold in the fresh blackberries. Toss them lightly with a spoon to distribute without crushing.
Spoon batter into cupcake liners, filling about 2/3 full.
Bake for 18-20 minutes or until a toothpick inserted in the center comes out clean. Avoid overbaking to keep cupcakes moist.
For the filling, beat softened cream cheese, powdered sugar, and lime juice until smooth. Taste and add a touch more powdered sugar if you prefer sweeter filling.
Once cupcakes have cooled, core the center using a small knife or cupcake corer and fill with the cream cheese mixture using a spoon or piping bag.
Top with extra blackberries, lime zest, and a slice of lime for garnish. Serve slightly chilled or at room temperature.
Notes
Store cupcakes in an airtight container in the refrigerator for up to 3 days. You can freeze unfilled cupcakes for up to 2 months.