Mix together butter, 1/2 cup sugar and orange zest, reserving orange for juice later in recipe, then eggs and vanilla. Scrape bowl and mix briefly. Add flour until just mixed, turn out on counter and knead once or twice to make sure it has come together in a cohesive mass.
Divide dough into thirds. Put dough in plastic bag. Use one third at a time and roll out to about 1/4 inch. Use cookie cutters and cut into your favorite shapes.
Bake 340 convection bake for 10 minutes (will take longer on regular bake also use 350 for regular bake). Edges should be lightly browned when taken out. Cool on a cookie rack
Make glaze from reserved Valencia orange juice. Start with 2 T of juice and add about a cup of powdered sugar until a thick glaze is formed. Spread glaze on cookies with a butter knife. Let dry overnight. Store in airtight container.