Line 2 baking sheets with parchment paper. Set aside.
In a stand mixer fitted with a paddle attachment, combine the powdered sugar, egg white product, 1 teaspoon water, peppermint extract and 1 to 2 drops of food coloring, if using. Mix on low speed until smooth. Increase the speed to high and beat until the mixture forms a stiff dough (if the mixture becomes too stiff, add extra water, 1/2 teaspoon at a time and beat until smooth). Put the mixture on a work surface dusted with powdered sugar and roll it into a log about 12-inches long and 1 1/4-inches in diameter. Slice the log into 1/4 to 1/2-inch pieces, form them into balls and flatten into discs. Arrange in single layers on the prepared baking sheets. Let the candies dry, uncovered, at room temperature for 3 hours.
Put the chocolate and vegetable oil in a small bowl and set it over a pan of barely simmering water. Stir until the chocolate is smooth and melted. Dip 1 half of each candy into the melted chocolate and return them to the parchment paper until the chocolate has set, about 3 hours.