You can leave the Bailey’s out entirely to make a kid-friendly version, or you can use an Irish cream-flavored syrup, like the kind they use at coffee shops.
Do a thickness check: take a rubber spatula and draw it down the middle of the batter in your pan to make a line. If it takes the mixture a few seconds to pool back over the line, you are ready.
Remove the pan from the heat and whisk in your vanilla extract and irish cream. Add a few drops of green food coloring until you reach your desired level of pigment.