Preheat oven to 325F (160°C) and line a 9x5 inch loaf tin with parchment paper.
Sift and mix dry ingredients (flour, salt, baking powder, and cinnamon) in a medium sized bowl and set aside.
Wash, peel, and core peaches (see notes on how to peel peaches). Place 2 peaches in a blender and puree until smooth (you may need to add 2-3 tbsp. of water if peaches are not too ripe/juicy). Transfer puree to glass jar and set aside.Dice the remaining peach into small pieces and set aside (do not leave large chunks as they will sink to the bottom of the cake). Place butter, brown sugar, and granulated sugar in a bowl of a stand mixer fitted with the paddle attachment and mix on medium speed for 1-2 minutes until creamy.
Add eggs, one by one, mixing for 1 minute after each addition. Add pureed peaches and mix for another minute until combined.
Slowly add dry ingredients, mixing on low speed until just combined. Do not overmix. Fold in diced peach using a spatula.
Pour cake batter into loaf tin and prepare topping.
Topping: Place butter in a microwave-safe bowl and heat in microwave until melted. Add flour, sugar, and cinnamon and stir until smooth.
Place dollops of topping over cake batter, and top with sliced peach. Sprinkle peach slices with some brown sugar as desired.
Bake in a preheated oven for 60-70 minutes or until golden brown at the top and a skewer inserted into the center comes out clean.
Allow to cool for 5-10 minutes in loaf tin, then transfer to a cooling rack to cool completely.¼