Preheat oven to 350F (180C) and grease the bottom of a nine-inch pan and line it with parchment paper.
Place the orange pieces and sugar in a food processor bowl and process until smooth, about one minute.
Add the olive oil and process.
Add the eggs, one at a time, and process until smooth.
Mix the flour, cardamom, and baking powder in a medium bowl. Add it to the orange mixture and pulse 3 times.
Pour the batter into the greased pan and bake on the medium rack shelf for 45-50 minutes. Or until a toothpick comes out from the center of the cake with a few moist crumbs.
Notes
Make sure all of the ingredients are at room temperature.
Use a kitchen scale to measure the ingredients, including the orange. If the orange is too small or too big, the cake might turn out too dry or too dense.
Taste the orange before baking with it. Choose an orange with a thin skin. The white pith should not be over 3mm.
Store the cake at room temperature for up to three days. To freeze leftovers, wrap the cake in plastic wrap, place it in a plastic bag, and freeze it for up to six weeks. When ready, allow the cake to defrost and unwrapped at room temperature.