Melt the butter in a large, shallow saute pan set over medium heat. Add the apples and cook for 2-3 minutes, or until slightly softened.
Add the rice; stir so that each grain of rice is coated with butter and appears glossy. Cook for 3-4 minutes, or until the rice is mostly translucent. Stir in the apple juice and cook until it has been absorbed.
Add 1 cup of almond milk along with the raisins, flax meal, chia seeds, and salt. Stir constantly until all the milk has absorbed into the rice. Continue this process, adding the milk 1/4 cup at a time, until the rice is creamy and soft – the whole process will take about 30 minutes.
Top with brown sugar, chopped apples, and walnuts, as desired.