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

Stir dried cherries and amaretto liqueur together in a saucepan over medium heat until the liqueur 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 using an electric mixer until light and fluffy, about 2 minutes.

Beat 3 eggs into the butter-sugar mixture one at a time, blending after each addition. Stir reserved cherry liquid and vanilla extract into the wet mixture.

Stir the dry mixture into the wet mixture gradually to form a smooth dough.

Gently fold cherries and almonds into the dough. On a floured surface, divide dough in half and form each half into a log (12 inches long, 2 1/2 inches wide). Press logs to about 3/4-inch thickness.

Transfer logs to prepared baking sheets. Brush with beaten egg and sprinkle each with 1 1/2 tablespoons of sugar.

Bake in the preheated oven until loaves are golden brown, about 35 minutes. Cool loaves on wire racks for 20 minutes.

Slice each loaf diagonally into 16 pieces. Place slices back on baking sheets. Reduce oven temperature to 300°F (150°C).