Strain the ricotta
Line a large strainer with two layers of cheesecloth, place the ricotta cheese on top and wrap the cheesecloth around the ricotta. Place something heavy over the cheesecloth and press firmly to help squeeze out the liquid. Place the strainer in a mixing bowl that leaves at least an inch of space between the bottom of the strainer and the bottom of the bowl. Place in the refrigerator and allow the ricotta to strain at least 4 hours or overnight.
Prepare the cake layers
Preheat oven to 350F (175C) and thoroughly grease and flour your cake pans. I recommend lining the bottoms of your cake pans with parchment paper rounds. Set aside.
In a large bowl or the bowl of your stand mixer, combine flour, sugars, baking soda, baking powder, and salt.
With an electric mixer on low speed, or your stand mixer, add butter one tablespoon at a time, waiting for each tablespoon to be fully incorporated before adding the next. Once finished the mixture should have a slightly sandy texture.
In a separate bowl whisk together buttermilk, eggs, and vanilla extract until combined.
With mixer on low speed, slowly pour buttermilk mixture into batter until combined and batter is smooth and silky. Be sure to pause and scrape the sides and bottom of the bowl as needed while mixing.
Evenly divide the batter into the prepared cake pans and bake in preheated oven for 28-30 minutes.
When cakes are finished baking, a toothpick inserted into the center should come out clean or with only a few moist crumbs.
Allow cakes to cool in pan for 10-15 minutes in pan before running a knife along the edge to loosen them up and inverting onto a cooling rack. Cool completely before frosting.
Frosting
Remove ricotta and mascarpone from the refrigerator 15-20 minutes before beginning so they have some time to soften but do not become too warm.
Combine drained ricotta and mascarpone cheese in a large mixing bowl and use an electric mixer on low speed to stir until smooth.
Gradually add powdered sugar until combined and smooth.
Add vanilla, cinamon, and salt and stir to combine.
Assembly
If necessary, level your cooled cakes. Spread an even, moderately thick layer of frosting over the first cake layer. Sprinkle 2-4 Tablespoons of mini chocolate chips evenly over the frosting. Take your next layer of cake and repeat this process. Top with the last layer of cake and cover the entire top and sides of the cake with an even layer of the remaining frosting (see decorating note below). Press the remaining mini chocolate chips about ⅓ of the way up from the bottom of the cake, and sprinkle some on top, if desired.