Heat oven to 350ºF with rack set in middle position. Grease 9-inch springform pan (if your springform pan is prone to leaking, wrap the base in a piece of foil). 

Whisk together flour, baking powder, and salt in bowl; set aside.

Using stand mixer fitted with the whisk attachment, whip eggs on medium speed until light foamy, about 1 minute. 

With mixer running, add sugar, 2 tablespoons minced orange zest, and vanilla. Increase speed to high, and whip until mixture is fluffy and pale yellow, about 3 minutes. 

Reduce speed to medium and, with mixer running, slowly stream in oil; mix 1 minute.

Reduce speed to low and add half of the flour; mix until incorporated, about 1 minute, scraping down side of bowl as needed. Stream in milk and grand marnier and mix until combined, about 30 seconds. Add remaining flour mixture and mix just until incorporated, about 1 minute, scraping down side of bowl as needed. (and scraping zest from white tines)

Transfer batter to prepared pan; evenly sprinkle top with about 2 tablespoons sugar. Bake cake until top is deep golden brown and a toothpick inserted in the center comes out with few crumbs attached, 48–50 minutes. Transfer pan to wire rack and let cool for 20 minutes. Remove side of pan and let cake cool completely, about 1½ hours. 

Meanwhile, peel and segment reserved zested oranges; squeezing juice from membrane over orange segments. Toss orange segments with cardamom. 

Using a stand mixer or hand mixer, beat heavy cream in a chilled metal bowl until bubbly. With mixer running on medium speed, stream in 2 tablespoons sugar, increase speed to high and whip until stiff peaks form. 

Spread whipped cream over cooled cake and top with oranges; cut into wedges and serve with additional olive oil.