For the almond cream: Add the butter, almond paste, rum, flour, almond extract and egg to the bowl of a stand mixer fitted with the paddle attachment and mix until smooth, 1 to 2 minutes. Set aside.
For the streusel: Add the butter, flour, oats, turbinado sugar, brown sugar, cinnamon and salt to the bowl of a food processor fitted with a metal blade. Pulse until the ingredients become a coarse crumb and set aside.
To build: Cut each croissant in half lengthwise and place cut-side up on a parchment-lined sheet pan. Brush the cut sides of the croissants with the simple syrup, about 1 teaspoon per half. Equally distribute the almond cream on the croissants followed by the blueberries, and sprinkle the streusel over the top.
Freeze, uncovered, until totally set, at least 2 hours.
Remove from the freezer and wrap individually in plastic wrap (to keep the toppings on), then place in large plastic bags.
To serve: Preheat the oven to 350 degrees F. Take the croissants out of the plastic bags, remove the plastic wrap, place on a baking sheet and bake until the almond cream has set and the streusel is golden, 15 to 17 minutes.
Remove from the oven. Sprinkle with the powdered sugar and serve hot or at room temperature.
Yield:1 1/2 cups
Pour 1 cup water into a saucepan and add the granulated sugar. Stir and place the saucepan over medium heat.
By the time the edges start to simmer, the sugar should have dissolved and the liquid should be completely clear, not cloudy. Immediately remove from the heat and cool completely.
Store the simple syrup in an airtight container, in the fridge, until ready to use. Simple syrup stays fresh up to 4 weeks.