Preheat oven to 375°F. Line a 9-inch cake pan with a circle of parchment paper and grease with canola oil spray, set aside.
In a medium bowl, sift together flour, sugar, salt, baking powder, and baking soda. Set aside.
In the bowl of a stand mixer or in a large bowl with a hand mixer, beat eggs at medium speed. Continue mixing while slowly adding olive oil for 2-3 minutes, until mixture thickens.
Add milk, clementine juice, and 1 tablespoon clementine zest and mix just until combined.
Add dry ingredients to egg mixture and beat on low speed just until combined (batter will be thin). Pour batter into greased pan.
Bake on center rack of oven for 45-50 minutes, rotating halfway through, until cake is a dark golden brown and a toothpick inserted into the center comes out clean.
Let cake cool 2 hours before removing from pan and frosting.
In the bowl of a stand mixer or in a large bowl with a hand mixer, add butter, powdered sugar, vanilla paste, milk, and salt.
Beat on low speed until powdered sugar is incorporated, then increase speed to medium for 2 minutes. Add more milk if necessary, to reach a spreadable consistency.
Unmold cake and remove parchment from bottom. Place cake on a serving platter or cake stand. Frost cake, garnish with remaining zest, and serve. Cake can be covered and stored on the counter for up to three days.
