In a small bowl, combine the flour, brown sugar, and melted butter. Mix with a fork until the mixture becomes crumbly with small and large clusters. Set aside while you prepare the batter.
In a large bowl, whisk together the flour, baking powder, baking soda, and salt until evenly combined.
In another bowl, whisk together the melted butter, granulated sugar, and eggs until smooth. Add the cooled coffee, buttermilk, Greek yogurt, and vanilla extract, then whisk until fully combined.
Add the dry ingredients into the wet ingredients. Using an electric hand mixer, beat briefly for about 30–60 seconds until the batter is smooth and combined. Avoid overmixing.
Preheat the oven to 220°C. Line your muffin tray with paper liners. Fill each muffin cup almost full for bakery style muffin tops. Generously sprinkle the crumble topping over each muffin.
Bake at 220°C for 5–6 minutes, then reduce the oven temperature to 190°C and continue baking for 14–18 minutes until the muffins are golden and a toothpick inserted into the center comes out clean.
Allow the muffins to cool in the pan for a few minutes before transferring to a wire rack. Serve warm with a hot cup of coffee or tea.