Step 1: Preheat your oven to 325°F (165°C). Ensure you have a 10-inch tube pan ready, but do not grease it.
Step 2: In a large bowl, sift together the cake flour, 1 cup of sugar, baking powder, and salt.
Step 3: In a separate bowl, whisk together the egg yolks, vegetable oil, blueberry puree, and vanilla extract until smooth.
Step 4: Gradually add the dry ingredients to the yolk mixture, whisking until just combined and no lumps remain.
Step 5: In a perfectly clean stand mixer bowl, beat the egg whites and cream of tartar on medium-high speed until foamy.
Step 6: Slowly add the remaining 1/2 cup of sugar while continuing to beat until the whites form stiff, glossy peaks.
Step 7: Gently fold one-third of the egg whites into the blueberry batter to lighten it. Then, fold in the remaining whites in two batches using a spatula, being careful not to deflate the mixture.
Step 8: Gently fold in the floured whole blueberries.
Step 9: Pour the batter into the ungreased tube pan and bake for 50-60 minutes, or until the top springs back when lightly touched and a skewer comes out clean.
Step 10: Immediately invert the pan onto its feet or a bottle and let it cool completely (about 1.5 to 2 hours) before removing the cake from the pan.