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Preheat the oven to 350° Fahrenheit and grease your loaf pan.
Brown all the butter for the cake and crumb topping (so 11tbsp total). To do this, melt it in a small saucepan over medium heat. Continue to cook for about 5-8 minutes, until it's got a golden hue and starts to smell a bit nutty. It'll also start to foam up. At this point, remove from heat and let it cool.
Once the brown butter has cooled down a bit, add 8 tbsp of it to the bowl of your stand mixer (or whatever large bowl you'll be using for this recipe) and put the rest in the fridge for later. Add 3/4 cups light brown sugar and mix until fully incorporated. Then add your eggs and vanilla extract and mix until combined.
Add the flour, salt, baking soda, baking powder, and cinnamon to a medium sized bowl and whisk to combine. Then add to the wet ingredients and mix until just incorporated.
Fold in the Greek yogurt, followed by the peaches, then transfer to your loaf pan.
Now make the crumb topping. To do this, add 1/2 cup light brown sugar, 1/2 cup all purpose flour, 1/2 tbsp cinnamon, and the rest of your brown butter to a bowl and mix with clean hands until it forms little crumbles. If it all clumps together, that's fine – just use your hands to crumble it! Pour all of the crumb topping into the loaf pan, making sure to coat all the batter evenly.
Bake for 50-55 minutes, or until you can insert a toothpick or knife into the center of the cake and remove it cleanly. Then let cool, slice and enjoy!