First, make your simple syrup. In a small saucepan, combine the 1/4 cup granulated sugar with the water and the rum. Bring to a boil, then reduce heat and simmer for 1 minute. Remove from heat and allow to cool completely.
Next, make your filling. In a bowl, whisk together the almond meal, granulated sugar, and salt until blended. Using a handheld electric mixer, beat in the butter until creamy, followed by the eggs, one at a time, and the extracts, whipping the mixture with the electric mixer until fluffy and smooth like a frosting consistency. Set aside.
Preheat oven to 350 degrees F. Place the croissants on a silicone liner or parchment paper. Using a pastry brush, brush the butterflied croissants with the simple syrup mixture. Using an offset spatula, add about 2-3 Tablespoons of the almond mixture to one half of the croissant and spread evenly. Top the almond mixture with the top part of the croissant to close it. Spread 1 Tablespoon of almond mixture over the tops of the croissants and immediately sprinkle with sliced almonds.
Bake for 15-18 minutes or until golden brown, sizzling and fragrant. Either cool on a wire rack until warm to the touch or cool completely before serving. These are best made and eaten the same day.