Stir together the mustard, garlic, thyme, and red pepper flakes in a small bowl to combine. Place the hanger steak in a large baking dish and season with salt and pepper. Spread the mustard mixture evenly all over the meat. Cover with plastic wrap and let marinate in the refrigerator for at least 2 hours, or overnight.
Heat the vegetable oil in a large skillet over medium-high heat. Add the steak and cook for 5 to 8 minutes per side, until cooked through. Transfer to a cutting board, tent with aluminum foil, and let rest for 10 minutes.
Stir together the tomatoes, onion, jalapeño, and cilantro in a small bowl and season with salt and pepper, to taste.
Scoop the flesh of the avocado into a small bowl and mash with a fork until smooth. Stir in the lime juice and season with salt, to taste.
Melt the butter in a medium skillet over medium-low heat. Whisk together the eggs, milk, ½ teaspoon of salt, and ¼ teaspoon of pepper in a small bowl. Add the eggs to the skillet and cook for 5 to 6 minutes, folding gently with a rubber spatula, until soft curds form.
To assemble the tacos, slice the hanger steak into thin slices. Divide the steak and scrambled eggs between the tortillas. Top with the pico de gallo and mashed avocado.