Preheat oven to 350°F with rack in middle.
Bake bread cubes in 1 layer in a large shallow baking pan until golden-brown, about 10 minutes.
Tear or cut mushrooms lengthwise into 1/4-inch-thick pieces.
Cook shallot in butter in a 12-inch heavy skillet over medium heat, stirring occasionally, until beginning to soften, about 3 minutes. Add mushrooms, 1/2 teaspoon salt, and 1/4 teaspoon pepper and cook until liquid mushrooms give off has evaporated, about 15 minutes. Add parsley and garlic and cook, stirring, 2 minutes. Remove from heat.
Whisk together half-and-half, eggs, cheese, 1/2 teaspoon salt, and 1/4 teaspoon pepper in a large bowl. Stir in mushrooms and bread cubes until coated well and let stand 10 minutes for bread to absorb some of egg mixture.
Meanwhile, butter ramekins, then put a round of parchment in bottom of each and butter parchment.
Spoon mixture into ramekins and bake on a baking sheet until firm to the touch, 30 to 35 minutes. Unmold puddings and discard parchment.