Prep the eggs: Boil eggs 9 to 10 minutes for fully hard yolks, cool in an ice bath for 2 minutes, peel, and set aside. Slice lengthwise if desired, halved eggs absorb the escabeche sauce better and look beautiful plated.
Sauté the aromatics: Heat olive oil in a medium skillet over medium heat. Add sliced red onion and green pepper. Sauté 3 to 4 minutes, stirring occasionally, until the onion is translucent and just beginning to soften. The goal is tender-soft, not browned.
Build the sazón: Add minced garlic and chopped tomatoes. Cook 2 more minutes, stirring, until the tomatoes begin to break down and release their juices.
Create the escabeche sauce: Stir in tomato paste, apple cider vinegar, salt, and pepper. Add the water or bone broth slowly, stirring to incorporate. Reduce heat to low and simmer 5 minutes until the sauce thickens and the flavors fully meld, it should coat a spoon and smell deeply savory with a bright acidic lift.
Stew the eggs: Gently nestle the hard-boiled eggs into the sauce. Spoon the sauce and onions over the eggs generously. Let them simmer together 2 to 3 minutes, just enough for the eggs to absorb the flavor and warm through completely.
Finish and serve: Garnish with plenty of fresh cilantro. Serve immediately directly from the pan, or plate over cauliflower rice with fresh avocado alongside.