In a medium skillet, add 2 tablespoons avocado oil over medium heat. Add diced shallot and cook, stirring, for 2 minutes. Add in minced garlic and cook another 1 to 2 minutes.
Reduce heat to low and add in capers, along with zest of 1 lemon and juice of half a lemon. Reserve other lemon half for serving. Stir until heated through, about 3 to 5 minutes, until peppers are cooked through but not soggy.
Stir in fresh parsley and season with a pinch of salt and pepper. Remove from heat until ready to serve.
In a large skillet, heat other 2 tablespoons avocado oil over high heat. While oil is heating, use a paper towel to dry haddock filets. Season both sides with salt and pepper.
Once oil is heated, add haddock, skin side down, and cook for 4 minutes. Use a fish spatula to carefully flip the filets and cook for an additional 2 to 3 minutes.
Plate filets, skin side down, and top with a few tablespoons of Red Pepper Caper Relish. Serve with vegetables of your choice and a wedge or slices of reserved lemon half.