Simmer potatoes, water, and 1/4 teaspoon salt in deep 12-inch skillet. Cover; cook over medium-low 7 to 9 minutes until nearly tender.
Uncover; evaporate water 2 minutes. Add 1 tablespoon oil; brown potatoes 6 to 8 minutes, turning occasionally. Transfer to bowl.
Add remaining oil, beef, and onion; cook over medium-high 7 to 8 minutes, crumbling beef, to 160°F. Spoon off excess fat.
Stir in garlic, remaining salt, and pepper 30 seconds. Add ketchup, mustard, and broth; simmer 2 minutes, scraping browned bits.
Fold in potatoes; warm 2 minutes. Scatter cheddar evenly; cover over low 2 minutes until melted.
Remove from heat; scatter pickles. Divide into 4 portions, keeping potatoes intact.