Cut the bread into 1-inch cubes. Let the cubed bread sit out uncovered for a few hours or up to 24 hours. (If you don’t have enough time, see Notes section below.)

Grease a 9×13-inch baking pan (or any 3–4-quart baking dish) with nonstick spray. Spread the bread cubes in the pan. Sprinkle the raisins and/or cinnamon chips evenly over the bread cubes.

In a large bowl (preferably with a pour spout), whisk together eggs, milk, cream, rum, granulated sugar, brown sugar, vanilla, cinnamon, and salt until combined. Pour evenly over the bread.

Cover the pan tightly and refrigerate for at least 4 hours or up to 24 hours. This gives the bread a chance to soak up the custard and is a key step in this recipe.

Remove bread pudding from the refrigerator and let it sit at room temperature for 10–15 minutes while you preheat the oven to 350°F (177°C).

Bake, uncovered, for 50–55 minutes, or until the center is set (no longer liquid-y). If the top of the bread pudding is beginning to brown too much, cover the pan loosely with aluminum foil.

Place the sliced butter in a medium saucepan over medium heat. Add brown sugar, and stir/whisk until melted and combined. Slowly pour heavy cream into the saucepan, whisking the entire time. Bring to a boil, then stop whisking and reduce heat to medium-low. Let the sauce simmer for 3 minutes. Remove from heat and whisk in the rum and salt. Let cool for at least 10 minutes to allow the sauce to thicken.

Remove bread pudding from the oven and cool for 5–10 minutes before serving. Bread pudding deflates slightly as it cools. Pour butter rum sauce all over the bread pudding, or serve each slice with butter rum sauce. Cut into slices and serve warm with ice cream, if desired.

Cover leftovers tightly and store in the refrigerator for up to 3 days.