Step 1

Arrange a rack in the middle of the oven and heat the oven to 350°F. Meanwhile, soft boil the eggs.

Step 2

Bring a medium saucepan of water to a rolling boil over medium-high heat. Gently lower in 4 large eggs and boil until the yolks are soft and jammy, about 7 minutes. Meanwhile, fill a medium bowl with ice water.

Step 3

Using a slotted spoon, transfer the eggs to the ice bath and let sit for 5 minutes. Remove from the water and peel.

Step 4

Split 4 English muffins. Tear into 1-inch pieces and place on a rimmed baking sheet. Drizzle with 2 tablespoons olive oil and season and 1/2 teaspoon kosher salt. Toss until evenly coated and spread into a single layer. Bake, rotating and flipping pieces halfway through, until toasted and golden brown, about 15 minutes total.

Step 5

Juice 1 medium lemon until you have 2 tablespoons. Chop 5 anchovies and 1 garlic clove together until the mixture is mostly smooth and paste-like. Finely grate 1 1/2 ounces Parmesan cheese (about 3/4 cup), or measure out 1/2 cup store-bought grated.

Step 6

Whisk 2 large egg yolks in a medium bowl until smooth. Add 1 teaspoon Dijon mustard and whisk until just combined. Add the anchovy-garlic mixture and whisk to combine. While whisking constantly, pour in the lemon juice and whisk until smooth.

Step 7

While whisking constantly, pour in 2 tablespoons olive oil to create a thick emulsion. Whisk for 1 minute longer to thicken. Continue whisking and slowly pour in 1/2 cup vegetable oil. Again, whisk for 1 minute longer to thicken. Add 1/2 cup grated Parmesan cheese and whisk to combine. Taste and season with black pepper as needed.

Step 8

Trim and cut 3 medium romaine lettuce hearts into bite-sized pieces and place in a large bowl. Add half of the dressing and toss to combine. Add the croutons and toss again. Use a vegetable peeler to shave some Parmesan on top as desired. Halve the jammy eggs vertically and place on the salad. Taste and season with more dressing, Parmesan, kosher salt, and black pepper as needed.