Heat oven to 350°F. Grease a 12-cup muffin pan with butter.
Whisk beaten eggs, milk, half-and-half, brown sugar, granulated sugar, vanilla, cinnamon, nutmeg, and salt until smooth.
Toss bread cubes with the melted butter in a large bowl.
Pour the custard over the bread. Stir to coat well, then let soak 8–10 minutes.
Spoon the mixture into the muffin cups, packing gently to fill each to the top.
Bake 20–24 minutes until puffed, golden, and set in the centers. Cool 5 minutes, then loosen and lift out to serve.