Bring sugar, corn starch, cocoa powder, milk, vanilla and kahlua to a simmer on stove top. Simmer until thickened (2-5 minutes). Remove from heat. Stir in butter.
Transfer liquid to bowl and let cool on counter for 15 minutes. Then cool in refrigerator for 15 minutes.
Pour into popsicle molds and freeze for about an hour. Add popsicle sticks while pops are slushy, but not firm. Freeze at least 3 more hours or until ready to eat.
Recipe by Talia Bunting at https://www.taliabunting.com/chocolate-white-russian-popsicles/