Preheat oven to 350°F. In a saucepan, bring 2 Tbsp. olive oil and garlic to a simmer; season with salt and pepper. Let stand off heat for 10 minutes. Remove and set aside garlic. On a baking sheet, toss bread with oil mixture. Toast for 15 minutes.
Mash anchovies and reserved garlic with side of a knife. Transfer to a bowl; whisk in vinegar, Worcestershire, mustard, and salt and pepper to taste. Whisk in remaining 4 Tbsp. olive oil until emulsified.
Toss romaine, dressing and croutons in a large bowl. Top with Parmesan curls.