Make the syrup: Combine all syrup ingredients in a small saucepan. Bring to a gentle boil, stirring until the sugars dissolve. Set aside and use while still warm.

Prepare the frangipane: In a food processor, blend together the almond flour, powdered sugar, and cornstarch. Add the softened butter and blend until smooth. With the processor running, add the eggs one at a time, then mix in the almond extract until creamy and well combined.

Assemble the croissants: Slice your day-old croissants in half horizontally. Dip each half lightly in the warm syrup, so they are web, but not soaked. Spread a layer of frangipane inside, sandwich them back together, then spread a little more frangipane on top. Sprinkle generously with slivered almonds.

Bake: Place the croissants on a lined baking sheet and bake at 350°F (175°C) for about 15–18 minutes, or until golden and crisp.

Finish: Allow to cool slightly, then dust with powdered sugar before serving.