Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, baking soda, ground cinnamon, and salt.
In a large bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy. Beat in the egg and vanilla extract until well combined.
Gradually add your dry ingredient mix into the wet ingredients. Mix until just combined. Gently fold in the diced peaches.
In a small bowl, mix together oats, melted butter, flour, brown sugar, and cinnamon to create your streusel topping.
Scoop tablespoons of dough onto your prepared baking sheet. Sprinkle each cookie with streusel topping before baking for about 13–15 minutes or until golden brown.