In a small bowl, sprinkle the yeast over the lukewarm milk. Stir briefly and allow to sit at room temperature until frothy, about 10 minutes.
In the bowl of a stand mixer fitted with a dough hook or a large bowl, rub the blood orange zest into the sugar until evenly infused.
Stir in the flour and salt.
Mix in the milk with the frothy yeast, egg yolks, egg, butter, and vanilla extract until a soft dough forms.
Knead on a lightly floured surface just until elastic and smooth. Place in a large bowl, cover, and allow to rest at room temperature until doubled, 1-2 hours.
On a lightly floured surface, roll the dough into a sheet about 3/4 inch (2 centimeters) thick.
Cut out circles (do not twist) with a 3 inch (7.5 centimeter) circular cutter. Bring together the scraps of dough and repeat to get as many doughnuts as possible.
Place the doughnuts 2 inches (5 centimeters) apart, cover with a towel, and allow to rise at room temperature until puffy, 30-60 minutes.
Pour 2 inches (5 centimeters) of vegetable oil in a large saucepan and heat to 340˚F (170˚C), no higher.
Once heated, gently add a few of the puffed doughnuts, taking care not to overcrowd. Immediately cover with a lid.
Fry until lightly golden on the bottom, about 2 minutes, then remove the lid and flip to fry uncovered until golden on the other side.
Transfer to a towel-lined platter and repeat with remaining doughnuts, keeping the temperature no higher than 340˚F (170˚C).
Allow the doughnuts to cool to room temperature before adding the blood orange cream cheese filling and covering with the glaze.