Place the peaches into a large bowl and toss with the cornstarch, 1 teaspoon of the cinnamon, and the lemon juice. Spread into the prepared baking dish.
Place the oats, flour, sugar, vanilla, remaining 1 teaspoon cinnamon into a medium bowl. Add the butter and yogurt.
Use your fingers to work the butter into the rest of the ingredients mixture to until uniformly mixed. There can be some chunks of butter remaining. The texture should be similar to a chunky granola. Alternatively, place the ingredients from Step 3 into a food processor and process to combine.
Spread the topping over the peaches in the pan. Bake for 45-50 minutes or until the peaches are bubbly and soft. If the topping starts to get too dark brown at any point, cover it loosely with a piece of foil and continue baking. Let cool slightly and serve warm or at room temperature.
Store any leftovers, covered, in the fridge for up to 5 days. Serve leftovers warm or cold with yogurt, ice cream, or whipped cream.
If using fresh peaches, slice them uniformly. You do not need to peel them. Fresh peaches should be ripe but still a little firm.
If using frozen peaches, you may need to bake for the longer time duration simply since they will start very cold.
Using fresh lemon juice will add a bright flavor to the fruit, making it taste ripe and fresh even if they weren't perfectly ripe!
Substitute almond flour or gluten-free flour blend for the whole wheat flour to make this gluten-free.