Place a rack in lower third of oven; preheat to 450°.

Whisk anchovies, garlic, 3 T mayonnaise, 1 T mustard, 1 T oil, and 1½ t pepper in a small bowl. Set aside 1 T anchovy mayo in another small bowl.

Pat chicken dry and season in and out with salt. Arrange breast side up in a cast-iron skillet and tuck wings underneath. Arrange shallots or a red onion around and brush well with anchovy mayo, except for the 1 T you set aside.

Place skillet in oven with legs facing towards the back. Roast for about 15 minutes until the anchovy mayo begins to drip on the shallots. Remove skillet from oven and turn over the shallots or onions to coat the other side in the drippings. Return skillet to oven for about 15 minutes being sure to check the chicken and shallots and turning and tossing the shallots until an instant-read thermometer inserted into the thickest part of the breast reads 155 degrees, about 45 – 55 minutes. Make sure shallots are soft and chicken is golden. If the chicken begins to get too dark, tent with aluminum foil.

Transfer chicken and shallots to a serving platter, leaving behind the juices and fat. Reserve skillet and reduce oven temperature to 400.

Finely zest 1/2 of 1 lemon into a large bowl. Cut lemon in half and squeeze in juice. Add reserved 1 T anchovy mayo, remaining 3 T of mayo, 1 T oo and whisk to combine then stir in Parmesan cheese. Season with salt and pepper and then set dressing aside.

Add bread to reserved skillet with fat and turn to coat. Return skillet to oven and toast bread, tossing halfway through, until golden brown and crisp, 12–15 minutes. Transfer croutons to bowl with reserved dressing. Add romaine and gently toss until lettuce is well coated. Season salad with salt and pepper.

Slice remaining lemon into wedges. Carve chicken and nestle back into skillet or transfer to a platter; arrange shallots and lemon wedges around. Serve with salad and more mustard alongside. As you can see I added the salad to the skillet and served this at the table.