CAKE: Preheat the oven to 350°F. Oil and flour an 8 inch round cake pan; line bottom of pan with parchment paper. In the bowl of a stand mixer fitted with the whisk attachment, beat eggs and sugar at high speed for 30 seconds. Add oil in a slow, steady stream, beating until combined. Add milk, beating until combined. Reduce mixer speed to low. Beat in vanilla paste. In a medium bowl, whisk together flour, baking powder, and salt. Gradually add flour mixture to egg mixture, beating until combined, stopping to scrape sides of bowl. Pour batter into the prepared pan. Bake until a wooden pick inserted in the center comes out clean, 30 to 33 minutes. Let cool in the pan for 5 minutes. Remove from pan, and let cool completely on a wire rack. Just before serving, brush with olive oil and top each slice with blood orange glaze.
GLAZE: Begin by juicing 3 blood oranges and reserve juice and pulp. Combine all blood orange juice, melted butter, and powdered sugar in a mixing bowl. Mix until all sugar is completely hydrated.