Heat the oven to 175 C / 350 F. Grease 6 cylindrical Runeberg torte molds, 6 cm / 2.5-inch, and dust lightly with extra crumbs.
Cream the softened butter and sugar in a mixing bowl for 2 to 3 minutes until pale and fluffy. Beat in the egg.
In a separate bowl, stir together the ground almonds, crushed rusk crumbs, flour, baking powder, and cardamom.
Add the dry mixture to the butter mixture in two additions, alternating with the milk and 1 tbsp rum. Mix in the almond extract until you have a smooth, thick batter.
Divide the batter evenly among the molds, filling each about two-thirds full. Smooth the tops with the back of a spoon.
Bake for 20 to 25 minutes, until a toothpick inserted in the center comes out clean and the tops spring back when pressed.
While the cakes bake, warm the sugar and water for the syrup in a small saucepan until the sugar dissolves, about 2 minutes. Remove from heat and stir in 1 tbsp rum.
Let the cakes cool in the molds for 5 minutes, then turn them out. Brush generously with the warm syrup while still warm and let them cool completely on a rack, about 15 minutes.
Whisk the powdered sugar with the water until you get a thick, pipeable icing. Transfer to a piping bag or a ziptop bag with the corner snipped off.
Pipe a ring of icing around the top edge of each cooled cake. Spoon a small dot of raspberry jam into the center of each ring and let set for 10 minutes before serving.