Combine the dry ingredients, — flour, baking soda, salt, ground cinnamon, and ground ginger — in a large mixing bowl. Whisk them together thoroughly and set the bowl aside.

In another bowl, blend the wet ingredients — sourdough starter, melted butter, brown sugar, granulated sugar, molasses, and egg — until the mixture achieves a smooth and creamy consistency.

Transfer the wet ingredients to the bowl containing the dry ingredients. Use a spatula or wooden spoon to carefully blend all the ingredients together. (Make sure the dough is smooth and not sticky. If it's sticky, mix in 2-3 tablespoons of flour.) Cover the bowl with plastic wrap or a lid and refrigerate the dough, allowing it to chill for at least one hour (up to 5 days).

When you're ready to bake, place the oven rack in the center position and preheat your oven to 350°F (176°C). Line a baking sheet with parchment paper or a silicone mat.

Place ¼ cup of granulated sugar on a plate or in a small bowl. Use a cookie scoop to measure out the cookie dough, with each portion being approximately 2 tablespoons. Take a portion in your hands and roll it to form a smooth ball. Roll the ball around in the sugar to evenly coat the outside of the dough ball.

Place 12 cookie dough balls on a baking sheet lined with parchment paper. Bake the cookies for 10-12 minutes until they spread and the tops begin to crack. Transfer the cookies to a wire rack to cool completely before serving them.