Preheat oven to 350°F (177°C). Grease a 9×5-inch loaf pan and line it with parchment paper.
For the topping, mix the 2 tablespoons light or dark brown sugar, 3 tablespoons wheat flour, 3 tablespoons rolled oats, and ¼ teaspoon ground cinnamon in a small bowl. Work in the 2 tablespoons unsalted butter until it sticks together a bit, then place in the fridge.
To make the bread batter, in a large bowl, whisk together the 2 cups whole wheat flour, 1 teaspoon baking powder, ½ teaspoon baking soda, and ½ teaspoon salt. In a separate bowl, whisk together the 1 large egg, ¾ cup granulated sugar, ⅓ cup unsalted butter, ½ cup yogurt, and ½ cup whole milk. Fold in the 2 cups chopped peaches. In a small bowl, whisk together the 1 tablespoon brown sugar and ½ teaspoon ground cinnamon.
Pour half of the batter into the prepared loaf pan, and smooth the top with a rubber spatula. Sprinkle the cinnamon and brown sugar evenly over the top, then finish with the remaining batter. Then sprinkle the crumb topping over it.
Place in the oven and bake for 60-65 minutes, until a tester inserted in the middle comes out clean. Transfer to a wire rack to cool for 30 minutes, then turn out of the pan to cool completely.
Notes
No need to peel the peaches, but you can if you want. You do you - leave the peel on or off. If you leave it on, give the peaches a good wash before prepping them if you leave on their skins.
Cut the peaches into small pieces. This means about ½-inch pieces, which will help the peaches blend into the batter without overwhelming it.
You won't need to toss peaches with flour. Some recipes recommend tossing fruit with flour first before folding it into a batter. I don't find that this makes much of a difference here, so I skip this step.
Rest the batter. Did you know that whole wheat flour, similar to gluten-free flours, likes a little hydration time? If you can, rest the batter while the oven heats.
It may take a bit longer to bake. Note that the 1 hour of baking time is a suggestion. You may need to bake the loaf a little longer because of the moisture in the peaches. Check every 5 minutes or so after 60 minutes.
Cover with foil. If you're concerned that the loaf is browning too quickly, cover it with foil.
Cool completely. While tempting to slice into it right away, let the loaf cool completely so that it's not too soft when you cut into it.
Use regular flour. You can absolutely use all-purpose flour here.
Dairy-free: Substitute the butter for non-dairy butter or oil, the yogurt for non-dairy yogurt, and the milk for non-dairy milk.