Preheat oven to 400 degrees. Butter and line a springform baking pan.
Remove fronds from fennel bulb (reserve) and chop bulb into thick wedges. Drizzle with oil and roast for 20 minutes, or until tender and slightly caramelized.
Transfer to a food processor or blender along with the eggs and sugar, and puree until smooth. Pour into a large bowl.
Lower oven heat to 350 degrees.
Stir in the almond meal, anise seeds, extracts, salt, and baking powder into the fennel and egg mixture and stir well until evenly combined. Pour into the prepared baking pan and bake 50 minutes to 1 hour or until set. Let cool in pan 20 minutes before removing sides and letting cool completely.
While cake bakes and cools, make the syrup: Combine the reserved fennel fronds, 1 ½ cups water, and 1 cup sugar and bring to a boil. Lower heat to a gentle simmer and let cook for about 20 minutes or until liquid thickens into a syrup. Strain syrup (discard fronds), and stir in anise extract and salt.
Brush warm syrup over cooled cake, allowing it to soak in. If desired, garnish cake with a few sprigs of fennel leaves or some additional toasted anise seeds.
Serve cake at room temperature.
