Whisk yogurt, milk, almond butter, maple syrup, vanilla and cinnamon in a large bowl until smooth. Stir in oats and peach pieces.
Divide evenly among six wide-mouth 16-ounce containers rated for freezer use, leaving at least 1 inch of headspace and staying below any glass shoulder.
Cover and refrigerate for at least 8 hours so the oats soften fully. Stir each portion, replace the lids and freeze for up to 2 months for best texture.
Move one container to the refrigerator 24 hours before eating and let it thaw completely at 40°F or below; do not thaw the jar on the counter or put frozen glass into hot water.
Stir well and eat cold from the container, or spoon into a bowl. Use the thawed portion within 24 hours and keep it refrigerated until serving.