Preheat oven to 350°. Coat a 9-inch springform pan with 1 Tbsp. softened unsalted butter.

Melt chocolate chips with brown sugar and butter in a saucepan over low heat. Stir frequently until chips are smooth, about 8 minutes.

Whisk together milk, eggs, vanilla, espresso powder, and salt and pour over bread cubes. Toss well so the bread absorbs most of the liquid and begins to lose its shape.

Fold melted chocolate into bread mixture, then transfer to the prepared pan. Bake for 1 hour, or until the center of pudding springs back when gently pressed. Cool on a rack for 15 minutes, remove sides of spring form pan, and slice pudding.