Crack the eggs into a separate bowl. Put the flour, baking powder and salt together in medium-sized bowl and whisk together for 30 seconds.
Place the sugar in a medium-sized blow and zest the blood oranges directly into the bowl on top of the sugar. Use your fingers to rub the zest and sugar together. This method better releases the oils and flavor of the orange zest into the cake batter.
For this cake you will need 1 cup in total of blood orange juice - 1/4 cup for the cake, 1/2 cup for the soaking syrup and about 1/4 cup for the glaze. After zesting your oranges juice them until you 1 cup of juice.
Place the butter in the bowl of a stand mixer and with the paddle attachment mix on medium speed for 1 minute. Scrape down the sides and bottom of the bowl.
Add 1/2 cup of the blood orange-sugar mixture and beat on medium speed for 1 minute, Stop the mixer, add another 1/2 cup of the sugar mixture and beat for 1 minute. Repeat this step until all the sugar is added. Stop after the 3rd addition and scrape down the sides and bottom of the bowl and the paddle attachment. After all the sugar is added beat the cream and sugar for 2 more minutes on medium speed.
Scrape down the sides and bottom of the bowl and the paddle attachment. Add the eggs one at a time and beat on medium speed until each egg is well incorporated, about 20 seconds. Stop the mixer after adding the first 3 eggs and scrape the bowl from the bottom to ensure the ingredients are well mixed. Add the remaining 2 eggs one at time and scrape the down the sides and bottom of the bowl after beating in the last egg.
Add 1/4 cup of blood orange juice and vanilla extract and mix on medium speed until well combined.
Add one-third of the dry ingredients and mix on low speed until well combined, but do not over mix. Add one-half of the sour cream and mix on medium speed until well combined. Add half of the remaining dry ingredients, then the rest of the sour cream, mixing after each addition. Add the remaining the dry ingredients and mix until just combined. Scrape down the sides and bottom of the bowl and mix on low speed for about 30 seconds to make sure the batter in well mixed.
Scoop the batter into the prepared bundt pan. Use an offset spatula to spoon the top of the batter. Next place a kitchen towel on the counter and bang the bundt pan 4-5 times to settle the batter in the groves of the pan and break up any air bubbles.
Bake for 55-65 minutes until a skewer inserted in the center comes out clean or if using an instant-read thermometer and take the temperature in the center of the cake. The temperature should be 203 degrees F.
Remove the cake from the oven and place on a cake rack. Cool the cake in the pan for 15 minutes and then invert onto a cooling rack. Brush the entire surface with the blood orange soaking syrup using all the glaze. Allow the cake to completely cool, about 90 minutes.