In a large bowl, whisk together the flour, baking powder, baking soda, and salt.
In the bowl of a stand mixer fitted with the paddle attachment (or using a bowl and handheld electric mixer), cream together the coconut oil, cream cheese, sugar, and vanilla bean until light and fluffy. Wiping down the bowl and beater as needed, beat in the eggs one at a time, until fully incorporated.
Whisk together the buttermilk and vanilla extract.
With mixer on lowest speed, mix in about 1/3 of the dry ingredients, followed by 1/2 of the liquids, mixing each addition in until mostly incorporated and continuing in this manner until all has been added. Add chopped kumquats and fold in by hand just until all ingredients are evenly combined.
Transfer batter to bundt pan, making sure to fill to all corners and edges, and smoothing out top lightly with a spatula. Firmly rap pan on counter a few times to ensure batter settles into pan evenly.
Bake in preheated oven for 50-60 minutes, just until a toothpick inserted all the way into the center of the cake comes out clean. Cool in pan for about 30 minutes, and then flip onto wire rack to cool completely.
Dust with powdered sugar before serving. Serve with vanilla bean whipped cream and candied kumquats, if desired. Cake is best at room temperature, but for longer shelf life, keep refrigerated.
Vanilla Bean Whipped Cream
Combine cream, sugar, and vanilla bean in the bowl of a stand mixer fitted with the whisk attachment (or in a bowl using a handheld electric mixer). Beat on medium-high speed until cream holds peaks.
*To quickly bring eggs to room temperature, place in a bowl and cover with warm water. Let sit for 5-10 minutes before using.