Whisk yogurt, milk, almond butter, maple syrup, vanilla, and cinnamon smooth in a large bowl. Stir in oats and peaches.
Divide among six wide-mouth, freezer-rated 16-ounce containers, leaving at least 1 inch headspace and staying below glass shoulders.
Cover; refrigerate at least 8 hours until oats fully soften. Stir portions, replace lids, and freeze up to 2 months for best texture.
Refrigerate one container 24 hours before eating to thaw completely at 40°F or below. Do not thaw on counter or put frozen glass in hot water.
Stir well; eat cold from container or spoon into bowl. Keep refrigerated until serving; use within 24 hours of thawing.