In a large bowl, add the beef and break it up a little. From high above the bowl for even coverage, sprinkle over the onion pulp, 1 teaspoon of the curry powder, the onion powder, 1 teaspoon salt, a few grinds of pepper and the thyme. Gently mix with your non-dominant hand until just combined. Form into 4 equal balls and let rest in the bowl. Drizzle with the olive oil, cover with plastic wrap and rest at room temperature 1 hour.
In a liquid measuring cup, whisk the tomatoes, ketchup, honey, hot sauce and the remaining 2 teaspoons curry powder until combined.
Preheat 4 personal-sized cast-iron pans over medium-high heat. Form each ball of beef into a patty and press each patty to fill the entire bottom of each pan; the patties will shrink as they cook. Cook until each patty easily lifts from the pan and a peek beneath reveals a golden-brown sear, about 5 minutes. Flip the patties, then immediately pour the tomato mixture evenly over each and jiggle the pans to settle the sauce.
Using the back of a spoon, gently press a recess in the center top of each patty. Gently crack an egg into the center of each patty, resting the yolk in the recess you created. Cover all the pans with a large baking sheet. Reduce the heat to a low simmer and leave covered until a quick peek beneath reveals the whites are cooked and the yolks are still runny, about 3 minutes. Garnish each with a tiny sprinkle of salt over the yolks, a grind of pepper and a sprinkle of parsley.