Preheat the oven to 350°. In a small bowl, stir together the honey and tea; let cool. In a medium bowl, stir together the flour and baking soda. In a large bowl, using a handheld mixer at medium-high speed, beat half of the granulated sugar with the egg yolks until thick and pale, about 2 minutes. Slowly drizzle in the olive oil, beating until thickened, then beat in the honey-tea mixture and the dry ingredients in alternating batches.
In another medium bowl, beat the egg whites until soft peaks form. While beating, gradually add the remaining granulated sugar and beat until stiff peaks form. Fold the egg whites into the batter until no streaks of white remain. Pour the batter into an ungreased 10-inch angel food cake pan. Smooth the top and bake for 45 to 50 minutes, until the top is dark golden brown and a toothpick inserted in the middle comes out clean. Immediately invert the cake pan onto a wire rack and let the cake cool completely.