Line cookie sheets with parchment paper or foil. With a mixer, beat butter on high for 3 minutes or until very soft and light in color. Add grated almond paste and sugar, mix on low speed until combined. Turn mixer to high and beat a full 5 minutes or more, until just combined. Spoon 1/2 of dough onto a 15-inch long piece of wax paper. With hands, press dough out to 1/4-inch thickness. Top with wax paper. Lightly smooth top with rolling pin, keeping wax paper in place, lay dough on cookie sheet. Repeat with remaining half of dough. Chill for 1 hour to firm.
Preheat oven to 325°F shortly before removing dough from chilling in the fridge. Work with 1 piece of dough at a time, keeping other half chilled. Cut out the cookie sheets, shamrocks or other shapes. Place on cookie sheets 2-inches apart, dipping cutters in flour if sticking. Repeat until dough is used. Keep unbaked cookies chilled till ready to bake.
Bake plain or brush tops with milk and sprinkle with colored sugar. Bake for 12 to 14 minutes or until cookies are firm and bottoms are very light golden. Cool on wire racks. Store in air tight containers with parchment paper between layers.