Oooh, Amy... lots of good ideas on this one! You could just use a regular star cookie cutter and then use a knife to cut the pattern (as shown in the photo above in your post.) Or use a smaller star cookie cutter to remove the middle (left hand picture below) or just make an impression in the middle (to add interest to your stars). Or add glass beads instead of paint (right hand photo). Obviously, the glass beads as shown would be too small to use with young children. And, don't use plastic beads as they'll melt in the oven!
Left photo from The Best Ideas for Kids
Right photo from The Artful Parent