Using a pastry blender or your fingers, cut the butter into the flour mixture until the mixture is mealy with pea-sized lumps.
Add the ice water and knead the dough slightly to bring it together and form a ball.
Chill dough for 30 minutes.
Combine the almond paste and sugar (it will be very stiff so you will have to mix it with your fingers); add the egg and mix until well-combined.
To Make Tarts.
Pull off enough dough to make a 1/2 to 3/4-inch ball.
Place ball of dough into cup of non-stick or lightly greased muffin/tart pan (with 1 to 1 1/2-inch sized cups).
Using a tart shaper (dipped in flour to prevent sticking) press into center of ball, flattening the bottom and forcing dough up sides of muffin cup. If you don't have a tart shaper use your thumb or other rounded tool instead.
Be careful not to make dough too thin on bottom. Fill in any accidental thin spots with small pieces of dough pressed into place.
Repeat for remaining muffin cups.
Return any remaining dough to refrigerator until ready to make next batch to keep it from getting to soft.
Place almond filling in pastry bag or plastic bag with a hole cut in one corner and pipe filling into pastry cups, filling them up about 3/4 of the way full (filling with puff up some during baking).
Bake 15-20 minutes, or until crust is lightly browned.
Let cool in pan before removing tarts.
If desired, spinkle tops with powdered sugar after cool.