Preheat the oven to 350°F.
Coat the peeled garlic cloves in oil, wrap in foil and roast for about 20-30 minutes, until caramelized.
Toss the bread cubes with the olive oil, minced garlic, salt and pepper on a baking sheet. Toast until crispy, 8-10 minutes. Cool.
Add the roasted garlic, lemon juice, anchovies, mustard, vinegar, mayo, Worcestershire sauce, and parmesan to a blender, food processor, or immersion blender. Blend until smooth. As the mixture is blending, slowly add the oil to emulsify. Season to taste.
Toss the romaine with the dressing and croutons in a large bowl. Garnish with Parmigiano-Reggiano.