Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans and line the bottoms with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
In a large bowl, beat the softened butter and sugar until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Gradually add the dry ingredients to the wet ingredients, alternating with the milk, beginning and ending with the flour mixture. Mix until just combined.
Gently fold in the mini chocolate chips.
Divide the batter between the two cake pans and smooth the tops with a spatula.
Bake for 25–30 minutes, or until a toothpick inserted into the center comes out clean. Let the cakes cool in the pans for 10 minutes before transferring them to a wire rack to cool completely.
To make the filling: In a large bowl, beat together the ricotta cheese, mascarpone cheese, powdered sugar, and vanilla extract until smooth and creamy.
Gently fold in the mini chocolate chips.
Once the cakes have cooled, place one layer on a cake stand or serving plate. Spread a generous layer of the cannoli filling over the cake, smoothing it into an even layer.
Place the second cake layer on top, gently pressing down.
Spread the remaining cannoli filling on top and around the edges of the second layer.
Garnish with chopped pistachios around the edges of the filling, if desired.
Dust the top of the cake with powdered sugar and sprinkle extra mini chocolate chips on top.
Slice, serve, and enjoy!