Set your oven to 375°F for preheating. Grease 4 wells of a muffin tin. You can alternately use paper liners.
Combine flour, 4 tablespoons of the brown sugar, baking powder, flax, and salt in a large bowl. Stir well to to make sure everything is well combined.
Pour almond milk, oil, and vanilla into a measuring cup.
Add the liquid ingredients to the dry ingredients. Stir until just combined. Do not overmix the batter.
Gently add in the diced peaches. Mix together gently so not to break up the peach bits.
Fill the muffin tins to about ¼ inch from the top.
Sprinkle the remaining tablespoon of brown sugar evenly across the tops of the batter.
Bake the muffins for 20-23 minutes. Check with a skewer inserted in the center to see that it comes out clean.
Allow the muffins to cool for at least 15 minutes before removing them from the muffin tin.