Preheat oven to 350 degrees Fahrenheit (175 degrees Celsius) and grease three 8-inch round cake pans.
In a large bowl, cream together the butter and granulated sugar until light and fluffy.
Add eggs one at a time, beating well after each addition, then mix in the pistachio paste and vanilla extract.
In a separate bowl, whisk together cake flour, baking powder, and salt.
Gradually add the dry ingredients to the wet ingredients, alternating with milk, starting and ending with the flour mixture.
Divide batter evenly between pans and bake for 30 to 35 minutes or until a toothpick inserted comes out clean. Cool cakes completely.
In a medium bowl, whip the drained ricotta cheese with powdered sugar and cinnamon until smooth and creamy.
Fold in the mini chocolate chips and half of the crushed pistachios into the ricotta mixture.
Place one cake layer on a serving plate, spread a thick layer of ricotta filling, and repeat with remaining layers.
Frost the top and sides of the cake with the remaining filling or a stabilized whipped cream.
Press the remaining crushed pistachios onto the sides of the cake for decoration.