1. Heat oil in a large deep skillet over high heat. Add onions and cook, stirring, until golden brown and tender, about 5 minutes. Add mushrooms, garlic, 1 1/2 teaspoons Essence, 1 teaspoon salt, and 3/4 teaspoon pepper. Cook, stirring, until mushrooms are tender and have given off any liquid, 3 to 5 minutes. Add beer to deglaze pan and cook, stirring, until mixture is almost dry, 1 to 2 minutes. Remove from heat and let cool.

2. In a large bowl, whisk together eggs, cream, molasses, Worcestershire sauce, thyme, remaining 1 1/2 teaspoons Essence, remaining 1/2 teaspoon salt, and remaining 1/4 teaspoon pepper until well combined. Add onion-mushroom mixture and cheeses; stir to combine. Add bread cubes and let stand until liquid is absorbed, about 2 hours.

3. Preheat oven to 350 degrees.

4. Butter a 9-by-13-inch baking dish; add bread crumbs, shaking baking dish to coat. Pour egg mixture into baking dish and cover with parchment paper-lined aluminum foil. Transfer to oven and bake for 1 hour. Uncover and continue baking until pudding rises, is firm in the center and golden brown, 20 to 30 minutes more. Let cool slightly before serving.