Melt butter and pour it over the dry mixture. To melt the butter, place it in a microwave-safe bowl, cover to prevent splattering, and cook at 50% power for 30 seconds. Stir and cook in 30 second intervals until melted. It should take about a minute, depending upon your particular microwave. The butter can also be melted on the stovetop.
Combine egg-replacer ingredients (baking powder, vinegar, and water) in a small bowl. Stir and add to cookie dough.
Stir the batter well to incorporate the ingredients. The dough should be wet and crumbly.
Place 12 heaping teaspoon-sized drops of batter onto a baking sheet lined with parchment paper. The cookies will spread while they cook so do not crowd them.
Bake for approximately 10 minutes or until the sides just begin to brown. The center will still be slightly soft.
Allow the cookies to sit on the baking sheet for at least 5 minutes (longer is okay) and then carefully transfer them to a wire rack to cool completely. The cookies will continue to firm up for the next hour until they become crispy.