Center the rack in the oven and preheat to 375°F (190°C). Line a 12-cup muffin tin with paper liners.
Place the muffin tin on a baking sheet.

For the streusel:
In a small bowl, combine the flour, brown sugar, and Jamaican pepper. Add the cold butter and mix until the mixture is crumbly, using your fingers to work the butter into the dry ingredients until it forms a uniform crumb. Refrigerate until ready to use.

For the muffins:
In a large bowl, whisk together the flour, sugar, brown sugar, baking powder, Jamaican pepper, and salt.
In another bowl, whisk together the melted butter, eggs, milk, and vanilla extract until well combined.
Pour the wet ingredients into the dry ingredients and stir until just combined. Fold in the lemon zest and apple cubes.

Divide the batter among the muffin cups and top with the reserved streusel.
Gently press the streusel into the batter.

Bake for about 25 minutes or until the tops are golden brown and a thin knife inserted into the center of a muffin comes out clean.
Transfer the muffins to a wire rack to cool for 5 minutes, then remove the muffins from the tin and let cool completely.