Preheat oven to 375°F (190°C) and position rack in the center. Lightly grease a 9x13 inch (23x33cm) baking dish with butter or non-stick spray, coating the corners and sides.
Wash and dry peaches. Slice each peach in half, remove the pit, and dice the flesh into approximately 1/2-inch (1.2cm) pieces (about 2 cups or 300g). Slice 8-10 additional peach wedges and set aside separately for the topping.
In a large mixing bowl, combine 3 cups (270g) old-fashioned rolled oats, 1 1/2 teaspoons baking powder, 1 1/2 teaspoons cinnamon, 1/4 teaspoon nutmeg, 1/4 teaspoon ginger, and 1/4 teaspoon fine salt. Whisk until evenly distributed.
In a medium mixing bowl, whisk 2 large eggs until combined. Add 2 cups (480ml) milk, 1/3 cup (80ml) maple syrup, 2 tablespoons melted butter (cooled slightly), 1 teaspoon vanilla extract, and 1/2 teaspoon almond extract. Whisk until smooth and uniform.
Pour the wet ingredients into the dry ingredients and stir with a rubber spatula until fully combined and no dry oat pockets remain. Let sit for 1-2 minutes to allow oats to absorb liquid.
Add the 2 cups (300g) of diced peaches to the oat mixture. Gently fold them in using a slow, scooping motion to distribute evenly without mashing the fruit.
Pour the mixture into the prepared baking dish and spread into an even layer, reaching the corners. Arrange reserved peach slices on top in a single layer, fanning them decoratively.
Bake on the center rack for 40-45 minutes until edges are golden brown, the center is firm and not jiggly, and the top peach slices have softened and caramelized. Tent with foil if top browns too quickly.
Remove from oven and rest for at least 5 minutes before slicing to allow the oatmeal to firm up fully. Cut into 8 squares (2x4 grid) and serve warm with desired toppings.