Preheat the oven to 400 degrees F (200 degrees C). Spray 18 muffin cups with cooking spray or line with paper liners.
Place milk and vinegar in a small bowl; stir and set soured milk aside.
Beat brown sugar, white sugar, and butter together in a bowl using an electric hand mixer or stand mixer until creamy and smooth. Add soured milk, eggs, egg yolk, and vanilla extract; beat until smooth, scraping down the sides of the bowl as needed.
Mix brown rice flour, white rice flour, flax seeds, baking powder, xanthan gum, cinnamon, and salt together in another bowl. Stir slowly into creamed butter mixture until just mixed. Stir in cranberries and walnuts.
Spoon batter into the prepared muffin cups, filling each about 3/4 full.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 18 to 20 minutes.