Toss bread with 2 tablespoons oil and 1/4 teaspoon each of salt and pepper in a large 4-sided sheet pan, then spread out in 1 layer. Toast in oven, stirring halfway through, until golden, 12 to 15 minutes.
Meanwhile, with motor running, drop garlic into a food processor and finely chop. Add egg, lemon juice, anchovy paste, and 1/2 teaspoon pepper and pulse until combined. With motor running, add remaining 6 tablespoons oil in a slow stream, blending until emulsified. Add herbs and blend until dressing turns green and herbs are finely chopped.
Toss romaine with dressing, croutons, and half of cheese in a large bowl. Sprinkle with remaining cheese.