Boil whole clementines for 2 hours until very soft. You may need to replenish the water as it evaporates. Cool, remove stems, then blend (skin and all).
Preheat oven to 375°F / 190°C. Line an 8-inch pan. Whisk eggs + sugar, then mix in almonds, baking powder, vanilla, salt, and clementine purée.
Pour into pan and bake 50–60 minutes until set. Cover loosely with foil if browning too quickly. Cool completely.
Thinly slice clementines. Boil in water for 3–5 minutes, then drain (this helps reduce bitterness).
Heat sugar + water until dissolved. Bring to a gentle simmer at 215–220°F (100–104°C). Add slices and simmer 15–20 minutes until translucent and glossy.
Transfer slices to parchment lined pan or a rack and let dry 6–8 hours or overnight.
Whisk powdered sugar, corn syrup, milk or cream, and vanilla until smooth and pourable.
Drizzle icing over cooled cake and top with candied clementines.
