1. Preheat the oven to 400°F (200°C). Line a 12-cup muffin tin with paper liners.

2. In a large bowl, cream the butter and sugar until light and fluffy. Beat in the eggs one at a time, ensuring each is fully incorporated before adding the next. Be careful not to overmix, as this can lead to tough muffins.

3. In a separate bowl, whisk together the flour and baking powder. Add half of the heavy cream (120 ml or 1/2 cup) to the dry ingredients along with the diced apple, and mix until just combined. Gently fold the wet ingredients into the dry ingredients until just incorporated.

4. Divide the batter evenly among the muffin cups, filling each about 2/3 full.

5. Bake for 10 minutes, then reduce the oven temperature to 375°F (190°C) and continue baking for 6 to 8 minutes, or until a toothpick inserted into the center comes out clean.

6. While the muffins bake, prepare the glaze by combining the remaining heavy cream (120 ml or 1/2 cup), sugar, and softened butter in a small saucepan. Bring to a boil, then reduce heat and simmer for 2 to 3 minutes until slightly thickened.

7. Remove the muffins from the oven and brush the warm glaze over the tops. Return them to the oven and bake for another 2 to 3 minutes until the glaze is set. Allow muffins to cool slightly before serving to avoid burns.