Mushroom and Speck Savory Bread Pudding

Name: Mushroom and Speck Savory Bread Pudding
Ingredients: Half loaf 8 oz, 225 gr of white bread (French, Italian...); three tablespoons of olive oil divided; 1 garlic clove; 3 large eggs; 2 cups 475 ml of milk (I used whole milk); 1 lb 450 gr of mushrooms (I used white mushrooms), washed and sliced; 3.5 oz 100 gr of speck (or pancetta), sliced thin; 2 tablespoons of fresh Italian parsley chopped; 1/2 packed cup 60 gr of shredded Gruyere cheese; 2 tablespoon of grated Parmesan cheese; butter for greasing; salt and pepper