1. In 2-quart saucepan over high heat, heat un-peeled potatoes and enough water to cover to boiling. Reduce heat to low; cover and simmer 25 to 30 minutes, until potatoes are fork-tender;drain. Cool potatoes until easy to handle; slice potatoes (do not peel). In small saucepan, hard-cook eggs.
2. Meanwhile, preheat broiler if manufacturer directs. Place round steak on rack in broiling pan. Broil steak 10 minutes for rare or until of desired doneness, turning once. Remove steak to cutting board; sprinkle with 3/4 teaspoon salt. With knife held in slanting position, cut steak into 1/8 inch-thick slices.
3. Remove shells from hard-cooked eggs. Separate yolks from whites; coarsely chop whites.
4. Prepare dressing: In blender at medium speed, blend hard-cooked egg yolks, olive oil, vinegar, mustard, sugar, basil, and 1/2 teaspoon salt until smooth.