In a small mixing bowl combine the flour, baking powder, salt and baking soda. Whisk to combine and set aside.
In the bowl of a stand mixer, combine the butter and 3/4 cup of sugar. Beat for several minutes or until light and fluffy, scraping down the sides as needed. Add the eggs, one at a time, beating well after each addition. Add the vanilla and blend until incorporated. Add 1/3 of the flour mixture to the creamed butter and sugar. Beat on low until incorporated. Add 1/2 of the ricotta and blend until smooth.
Repeat adding 1/2 of the remaining flour, then all of the remaining ricotta. Finally, blend in the remaining flour. Scrape down the sides of the bowl and fold gently with a spatula to ensure the batter is well mixed.
Pour 2/3 of the cake batter into the prepared pan and top with 2/3 of the raspberries. Layer the remaining batter on top of the raspberries and smooth the top with an offset spatula or the back of a spoon. Finally, scatter the remaining raspberries on top of the batter. Gently press the raspberries about halfway into the batter to secure.
Sprinkle the coarse sugar on top and bake in a preheated 325° oven for 60-75 minutes or until the top is lightly browned and a toothpick inserted in the center comes out with no wet batter, moist crumbs are fine. Cool at least 20 minutes before removing the sides of the pan.
Serve slightly warm or at room temperature garnished with fresh raspberries if desired.