Preheat oven to 350°F.
Cut the butter into 6 pieces to grease the mini loaf pans. Sprinkle a teaspoon of the cane sugar into each loaf pan, then shake the pan to coat the bottom and sides evenly, tapping the excess out into the sink.
In a large mixing bowl, whisk together the almond flour, baking powder and salt. Make a well in the center of the bowl. Add in the egg yolks, ¼ cup of the sugar and the vanilla, and whisk to combine. Incorporate the almond flour mixture from the sides of the bowl to form a stiff dough. Set aside.
In a stand mixer (or a large bowl with an electric mixer), whisk the egg whites at high speed until they form soft peaks. Turn the speed down to low and whisk in the remaining ¼ cup sugar.
Stir ⅓ of the egg whites into the almond flour batter until fully incorporated. Gently fold in the rest of the egg whites.
Spoon the batter into the mini loaf pans, distributing it evenly (about 5 tablespoons of batter for each pan).
Dollop 1½ teaspoons of jam onto cake. Use a butter knife to swirl the jam into the batter, taking care not to mix it all the way to the bottom of the pan.
Bake for 20 minutes. Allow the cakes to rest in their pan for 5 minutes, then carefully turn them out onto a cooling rack. Let cool to room temperature, about an hour.
* A single, 8-inch round cake pan may also be used, with the cooking time increased to 30–35 minutes.