This grilled Caesar salad delivers all of the classic flavors of the original plus adds smoky undertones from the grill. Grilling romaine brings out its natural sweetness, and charring the lemon caramelizes the sugars to make everything just a touch sweeter.
Whisk egg yolk, anchovy, mustard, garlic, Worcestershire, salt and 1/4 cup Parmesan together in a medium bowl until well combined. Whisking constantly, gradually add 1/3 cup oil. Cover and refrigerate until ready to use.
Preheat a gas grill to high (about 450°F to 500°F). Arrange romaine halves and lemon halves, cut-sides up, on a large baking sheet. Drizzle with the remaining 2 tablespoons oil and set aside.
Place bread on unoiled grates; grill, uncovered, until charred and crispy, 1 to 2 minutes per side. Transfer to a cutting board and set aside. Place romaine halves and lemons, cut-sides down, on unoiled grates; grill, uncovered, turning lettuce once halfway, until the lettuce is lightly charred on both sides and the cut sides of the lemons are charred, 2 to 4 minutes. Remove from grill; place romaine on a cutting board and slice in half lengthwise (making 8 wedges total).
Cut the charred bread into bite-size pieces. Juice 1 lemon half into the dressing mixture and whisk to combine.
Arrange the romaine wedges on a platter; drizzle with half the dressing mixture (about 1/4 cup) and top with the croutons. Juice the remaining lemon half over the salad. Sprinkle with the remaining 1 cup Parmesan. Serve immediately, with the remaining dressing.