Cook potatoes in their skins until tender. Let them cool a bit, cut into chunks. Cook asparagus and cut into pieces. Peel and cut each hard-boiled egg into 4 wedges. Make a dressing with basil leaves, olive oil, vinegar, garlic, and onion, all whizzed up in food processor. Toss potatoes and asparagus together in bowl and pour the dressing over (you might not need it all), turning gently to coat. Garnish with egg slices on top.