In a small saucepan over medium-high heat, melt all 3/4 cup of butter. Continue cooking, swirling occasionally, until the butter is foamy and turns a deep golden brown with a nutty aroma. You'll see the milk solids turn brown at the bottom, which is exactly what you want. This should take about 10-12 minutes. Pour the brown butter into a heat-safe bowl and let it cool for about 5 minutes.
Once cooled slightly, measure out 1/2 cup of the brown butter for the bread batter and set aside the remaining ~1/4 cup for the crumble topping.
In a large bowl, whisk together the 1/2 cup brown butter, light brown sugar, and granulated sugar. Mix for about 1 minute until well combined.
Add the eggs and vanilla extract to the butter mixture and mix for another minute until everything is smooth and creamy.
Add the pumpkin puree and milk to the wet ingredients and mix until fully combined and smooth.
In a separate medium bowl, whisk together the flour, baking powder, salt, pumpkin pie spice, and cinnamon. Make sure there are no lumps.
Gently fold the dry ingredients into the wet ingredients using a spatula, mixing until just combined. Don't overmix, as this can make the bread tough. The batter should come together with no streaks of flour visible.
Fold in the semi-sweet chocolate chips until evenly distributed throughout the batter.
Preheat your oven to 350 degrees Fahrenheit. Grease your 9x5-inch loaf pan or line it with parchment paper.
Pour the pumpkin bread batter into the prepared loaf pan and smooth the top with a spatula.
Now make the crumble topping by combining the remaining brown butter, light brown sugar, flour, and cinnamon in a small bowl. Mix until fully combined and the mixture looks like wet sand.
Stir in the mini chocolate chips until evenly distributed.
Crumble the topping mixture evenly over the pumpkin bread batter. Don't press it down, just let it sit on top loosely so it gets crispy and golden.
Place the loaf pan on a baking sheet (to catch any drips) and bake at 350 degrees for 65-75 minutes. At 65 minutes, insert a toothpick into the center. If it comes out clean or with just a few crumbs (not wet batter), it's done.
If the toothpick comes out wet, bake for another 5-10 minutes and check again. This bread is very moist due to the pumpkin, so it might take longer than 75 minutes. This is totally normal and fine, don't worry!
Once the toothpick comes out mostly clean, remove from the oven and let cool in the pan for 30 minutes before turning out onto a cooling rack.