Preheat oven to 400°F and set oven rack to the middle position.
Generously butter 12 non-stick muffin tins or line with paper liners.
In a small bowl combine flour, baking powder, cinnamon, salt, nutmeg and allspice. Set aside.
Melt butter and cream together with both sugars. Whisk in eggs one at a time until incorporated and light in texture. Stir in vanilla.
Add 1/3 of the milk and then 1/3 of the flour mixture whisking to combine. Repeat, alternating the milk and flour. Stir in grated apples and chopped pecans.
Scoop the batter evenly between the prepared muffin tins using approximately 1/3 cup of batter for each. The tins will be quite full.
Bake in preheated oven for 10 minutes at 400°F and then reduce the temperature to 350°F for an additional 8-10 minutes until a toothpick inserted in the center comes out clean.
Remove from oven and allow to cool for at least 10 minutes before removing to a cooling rack.