Preheat the oven to 350°F (175°C). Grease and flour a muffin pan or line with wrappers.
In a large mixing bowl, sift together the gluten-free flour, white sugar, salt, cinnamon, and baking soda.
Make a well in the center of the dry ingredients. Add the vegetable oil, beaten eggs, and vanilla extract. Stir until combined; the batter will be thick.
Gently fold in the chopped apples and walnuts (if using) until evenly incorporated.
Spoon the batter evenly into the prepared muffin pan. Bake for 40-50 minutes, or until a toothpick inserted in the center comes out clean.
While the muffins are baking, prepare the glaze. In a medium saucepan, combine the brown sugar, milk, and butter. Bring to a boil over medium heat, stirring constantly. Boil for 2 ½ minutes.
Remove the muffins from the oven and immediately pour the hot glaze over the top. Allow the glaze to soak in as the muffins cool.
Let the muffins cool in the pan for at least 15 minutes before serving. Enjoy warm or at room temperature.