If you have a decent food processor or blender, this cake. 1 lb of spent lemons can be substituted for the oranges. You could increase the sugar, or not, as you choose.
Edit- ignore the ‘don’t purée’ bit. Works fine with purée. I do mine in a vitamix
1 cup butter (225g), softened or browned
1 1/4 cups (250g) granulated sugar
3 large eggs
2 oranges (about 1 lb or 450g), ends trimmed, then cut into chunks and seeded
2 1/2 cups (315g) flour (if whole-grain, add 2 egg yolks)
1/4 teaspoon salt
1/4 teaspoon baking soda
2 teaspoons baking powder
Glaze
1 1/2 cups powdered sugar
2 tablespoons plus 1 tsp. orange juice
Preheat oven to 325°. Grease a 10-cup Bundt pan or 2 8x4 loaf pans. In a large bowl with a mixer on medium speed, beat butter and sugar until fluffy. Beat in eggs.
Whirl orange chunks in a food processor until mostly smooth but not puréed. Add 1 1/2 cups orange mixture to batter and beat until blended. Add flour, salt, baking soda, and baking powder to bowl and beat until smooth. Spread batter in prepared pan.
Bake until a toothpick inserted in the center comes out with only a few crumbs clinging to it, about 55 minutes. Cool pan on a rack 10 minutes, then invert cake onto rack and let cool completely.
Whisk together powdered sugar and orange juice in a small bowl. Drizzle over cooled cake. Let glaze set, then slice cake.
