In a large bowl or jar, combine oats, chia seeds, non-dairy milk, vanilla extract, and maple syrup (if using). Stir well. Cover and refrigerate overnight (or at least 4 hours).
In a small pan over medium heat, add the diced peaches and ½ teaspoon cinnamon. Cook for 3–5 minutes, stirring occasionally, until the peaches soften and release their juices. Remove from heat and let cool.
In jars or bowls, layer the chilled oats with yogurt and the cinnamon-spiced peaches. Repeat layers as desired.
Enjoy cold straight from the fridge or let sit at room temperature for 10 minutes before eating. Top with an extra sprinkle of cinnamon, if you’d like.