Preheat the oven to 375F. Line a 9-inch round, 3-inch tall springform pan with parchment paper. Coat with nonstick spray.
Sift together the flour, sugar, salt, baking soda, and baking powder. Set aside.
In the bowl of a stand mixer fitted with a whisk attachment, beat the eggs on medium speed. Stream in the olive oil and continue whisking until the mixture thickens slightly, 2-3 minutes. Stream in the oatmilk and orange juice. Mix until just combined. Add the orange zest.
Add the dry ingredients on low speed until just combined, about 30 seconds. Use a rubber spatula to scrape the bowl to ensure everything incorporated.
Pour the batter into the prepared springform pan. Bake until the cake begins to dome, about 25-30 minutes. Rotate the pan continue to bake until the top is golden brown and a toothpick comes out clean, 30-35 minutes. Meanwhile, make the brown butter buttercream.