Preheat the oven to 350°F (175°C). Grease and line a 9-inch cake pan with parchment paper.
Mix dry ingredients. In a bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.
Cream butter and sugar. In another large bowl, beat softened butter, olive oil, and sugar until light and fluffy.
Add eggs. Mix in the eggs one at a time, followed by vanilla extract, orange juice, and zest.
Combine wet and dry. Slowly fold in the dry mixture until just combined. Don’t overmix.
Bake. Pour the batter into the prepared pan and bake for 35–40 minutes, or until a toothpick inserted in the center comes out clean.
Cool and decorate. Let the cake cool completely on a rack, then top with orange slices and edible flowers for a simple garnish.