Preheat your oven to 375°F (190°C) and line a large baking sheet with parchment paper. Cut the day-old bread into 1-inch cubes and place in a large mixing bowl.
Stir together the olive oil, minced garlic, salt, and pepper in a small bowl, then pour over the bread cubes and toss until every piece is evenly coated.
Spread the coated cubes in a single layer on the prepared baking sheet and bake for 10–12 minutes, flipping once halfway through, until golden and crispy on all sides. Set aside to cool.
Separate, rinse, and spin or pat the romaine leaves completely dry, then tear or chop into bite-sized pieces and refrigerate until ready to use.
In a medium bowl, mash together the minced garlic and anchovy fillets into a smooth paste, then whisk in the lemon juice, Dijon mustard, and Worcestershire sauce until combined.
Add the 2 room-temperature egg yolks and whisk vigorously for about 30 seconds until the mixture looks smooth and slightly thickened.
While whisking constantly, add the extra virgin olive oil in a very slow, thin stream — almost drop by drop at first — until the dressing is thick, creamy, and fully emulsified.
Stir in the ¼ cup of freshly grated Parmesan, then taste and adjust with salt, pepper, or an extra squeeze of lemon juice as needed.
Drizzle about two-thirds of the dressing over the chilled romaine and toss thoroughly to coat every leaf, adding more dressing as desired.
Gently toss in the cooled croutons, then top with freshly grated Parmesan and a crack of black pepper. Serve immediately.