Old Fashioned Bread Pudding With Rum Sauce

Bread Pudding:

8 large eggs
3 1/2 cups milk
2 cups sugar
1 1/2 cups whipping cream
1 teaspoon vanilla extract
1 loaf cinnamon-swirl bread, cut into 1-inch cubes
1 cup chopped pecans
pinch salt

Rum Sauce:

1 cup (packed) brown sugar
1/2 cup (1 stick) butter
1/2 cup whipping cream
2 tablespoons rum (or spiced rum)
3/4 teaspoon ground cinnamon