Put potatoes, water and 1/4 teaspoon salt in a deep 12-inch skillet. Bring to a simmer, cover and cook over medium-low heat for 7 to 9 minutes until nearly tender.
Uncover and evaporate remaining water for 2 minutes. Add 1 tablespoon oil and brown potatoes for 6 to 8 minutes, turning occasionally, then transfer to a bowl.
Add remaining oil, beef and onion to the skillet and cook over medium-high heat for 7 to 8 minutes, breaking beef into crumbles, until it reaches 160°F. Spoon off excess fat.
Stir in garlic, remaining salt and pepper for 30 seconds. Add ketchup, mustard and broth and simmer for 2 minutes, scraping up the browned bits.
Fold potatoes into the beef and warm for 2 minutes. Scatter cheddar evenly over the top, cover and heat on low for 2 minutes until melted.
Remove from the heat and scatter diced pickles over the skillet. Divide into 4 portions, keeping the potatoes intact.