In a large saucepan, bring the water, butter, and salt to a rapid simmer.
Dump the flour in all at once and stir with a wooden spoon over low heat. The batter will come together as a thick dough, and the bottom of your pot will have a skim of dough stuck to it. Stir in the chopped almond paste. Stir and cook until it comes together in a smooth ball.
Place the dough into the food processor. (There’s no need to clean the bowl from when you used it earlier.)
Add the eggs one at a time, mixing well after each and scraping down the sides of the bowl, until it comes together in a smooth paste. Add the almond extract. The batter should be thick, but thin enough to spread easily.
Remove the plastic from the frozen dough and spread the Choux paste evenly over the frozen crust. Evenly sprinkle on the sliced almonds and pearl sugar.
Bake in the middle of the oven for about 30 minutes, until golden brown and very puffed. Allow to cool to room temperature in the baking pan. The kringle will seem to climb out of the pan while it bakes but will settle down as it cools.