Prepare anchovies. Place 2 anchovies in a mortar and grind with pestle until a smooth paste forms. Alternatively, you can chop the anchovies very finely with a knife. Place in a medium mason jar.
Make dressing. Add 1 tsp Dijon, 1 tsp lemon zest, juice from ½ a large lemon, 2 Tbsp parmesan cheese, 1 Tbsp minced garlic, and ½ cup olive oil. Secure lid on, then shake until well combined. Set aside.
Toast bread. Preheat oven to 375°F / 190°C. Combine 2 cups pumpernickel and 2 Tbsp olive oil on a large baking sheet, then toss to combine. Season with about 1 tsp kosher salt, then bake 7-9 minutes, or until crisp. Set aside.
Prepare the romaine. Heat a grill over medium-high heat (about 400°F / 205°C). Trim the tiniest amount off the ends of each romaine heart, just removing the part that is brown, then slice each in half lengthwise. Drizzle 2 Tbsp olive oil on the romaine.
Grill romaine. When grill is hot, grill romaine cut side down for about 2-3 minutes per side, or until charred and beginning to wilt. Remove and set aside.
Marinate the chicken. In a large mixing bowl or Tupperware, combine ¼ cup olive oil, 1 Tbsp salt, 1 Tbsp oregano, 1 tsp garlic powder, and ¼ tsp black pepper. Whisk to combine. Add chicken breasts and toss in marinade. Let sit for as long as you have time: 5 minutes, 30 minutes, or even overnight. The longer it sits, the better.
Cook the chicken. When ready, cook over medium-high heat on a grill (about 400°F / 205°C) for about 5-8 minutes per side (depending on thickness), or until internal temperature reaches 165°F / 74°C. Let rest 5 minutes, then cut into thin slices. Serve over grilled romaine with croutons and lemon wedges.