Do ahead: Cut and dry out the cinnamon roll pieces on a baking pan in a warm 250 degree oven, for about 20-30 minutes, cool completely.
In a small saucepan warm the butter, brown sugar, and 1/2 cup of the half-and-half on medium-low, stirring until melted and combined. Then remove from heat allow to cool.
In another bowl whisk together the eggs, remaining 1/2 cup of half-and-half, cinnamon, nutmeg and vanilla until well combined. Then whisk in the ingredients from saucepan.
Butter 12 muffin cups. Divide the cinnamon roll pieces among the muffin cups, piling them high. Pour 1/8 cup of the custard mixture over the cinnamon roll pieces in each muffin cup. Allow it to soak and absorb, add more custard as needed. Make sure the top layer has absorbed the custard too.
Sprinkle each muffin with pecans and sugar. Bake in the bottom third of oven for 35 minutes. When a knife comes out clean, they are done.
To make the glaze:
Stir milk into powdered sugar, 1 tablespoon at a time, until it is the consistency you like. Cool the muffins for 15 minutes. Remove from pan and drizzle with glaze. Serve warm.
The density and dryness of your cinnamon roll pieces may effect the amount of custard needed.