Double Chocolate Croissant Bread Pudding

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4 tablespoons unsalted butter, melted, plus more for the dish

8 croissants, sliced 1 inch thick (about 12 cups)

3 large eggs plus 3 egg yolks

1 1/2 cups whole milk

1 cup heavy cream

1/4 cup sugar

1 teaspoon pure vanilla extract

Pinch of salt

6 ounces milk chocolate, cut into 3/4-inch pieces

For the sauce:

cup heavy cream

2 tablespoons unsalted butter

2 tablespoons sugar

2 tablespoons light corn syrup

4 ounces bittersweet chocolate, chopped