Preheat oven to 375 degrees F (190 degrees C). Line 2 baking sheets with parchment paper.

Stir dried cherries and amaretto liqueur together in a saucepan over medium heat until the amaretto comes to a simmer; drain, reserving 2 tablespoons of the liquid for later use.

Sift flour, baking powder, and salt together onto a sheet of waxed paper. Beat butter with 1 cup sugar in a bowl with an electric mixer until light and fluffy, about 2 minutes. Beat 3 eggs into butter-sugar mixture, one at a time, blending in each egg before adding the next. Stir reserved cherry liquid and vanilla extract into the wet ingredients.

Beat butter with 1 cup sugar in a bowl with an electric mixer until light and fluffy, about 2 minutes. Beat 3 eggs into butter-sugar mixture, one at a time, blending in each egg before adding the next. Stir reserved cherry liquid and vanilla extract into the wet ingredients.

Stir flour mixture into the wet ingredients a little at a time to form a smooth dough. Gently fold cherries and almonds into dough. Turn the dough out onto a floured work surface, divide in half, and form each half into a log 12 inches long and 2 1/2 inches wide. Gently press the logs with your fingers to flatten to a thickness of 3/4 inch. Transfer loaves to the prepared baking sheets, brush with beaten egg, and sprinkle each with 1 1/2 tablespoon white sugar.

Bake in the preheated oven until the loaves are golden brown, about 35 minutes. Transfer loaves to wire racks and cool for 20 minutes. Use a sharp knife to slice each loaf on the diagonal into 16 pieces. Transfer the biscotti to baking sheets. Reduce oven heat to 300 degrees F (150 degrees C).

Bake in the oven for 8 minutes; flip biscotti and bake until crisp and lightly browned, about 8 more minutes.