Preheat oven to 350 degrees F. Butter an 8-inch round cake pan. Line bottom of cake pan with parchment paper.
Add butter to stand mixer. Beat on medium for 3 minutes.
Add granulated sugar to butter in stand mixer. Beat on medium for 2 minutes.
Add fresh ricotta cheese to sugar mixture in stand mixer. Beat on medium for 1 minute.
Add eggs one at a time to sugar mixture in stand mixer. Beat on low until fully incorporated, after each addition.
Add vanilla bean paste, fresh orange zest, and fresh orange juice to sugar mixture. Beat on low until fully incorporated, about 15 seconds. Scrape down the stand mixer bowl, if necessary.
Add all-purpose flour, baking powder, and fine sea salt to a small mixing bowl. Whisk to combine. Add half the flour mixture to the stand mixer. Beat on low just until incorporated. Add remaining flour to stand mixer. Beat on low just until incorporated. Do not over mix.
Transfer cake batter to prepared baking pan. Smooth top with small offset spatula.
Bake in preheated oven for 50 minutes. Top should be firm to the touch, and a toothpick inserted in the center should come out clean.
Remove baking pan from oven and place on wire rack to cool.
Once cool, invert the cake to remove from the baking pan. Remove parchment paper from bottom of cake. Cut individual slices for serving.
The orange ricotta cake can be stored in an airtight container for up to 3 days.