Preheat your oven to 350°F (180°C).
In the work bowl of a food processor, process chopped satsumas until almost puréed, about 30 seconds.
In a medium bowl, whisk together all-purpose flour, baking powder, and kosher salt.
In the bowl of a stand mixer fitted with the whisk attachment, beat granulated sugar and eggs at medium-high speed until thick and pale, 5 to 7 minutes.
With the mixer on medium speed, add melted butter and vanilla, beating until combined.
Add puréed satsuma, beating until fully combined.
Add the flour mixture and beat at low speed just until combined.
Spray a 10-cup Bundt pan with baking spray with flour.
Pour batter into prepared pan.
Bake until the top is golden brown and a wooden pick inserted near the center comes out clean, about 1 hour.
Let cool in pan for 10 minutes.
Meanwhile, in a small saucepan, bring satsuma juice and remaining granulated sugar to a boil over medium heat.
Invert cake onto a wire rack, and gently brush satsuma syrup all over cake.
Let cool completely on a wire rack.
Garnish with sliced almonds and Candied Satsuma Peels, if desired.