Whisk together vinegar, shallot, mustard, garlic paste, and anchovy paste in a small bowl until combined well, then add oil in a slow stream, whisking until emulsified. Whisk in thyme, basil, and salt and pepper to taste.

Cook beans in a 4- to 6-quart pot of boiling salted water , uncovered, until crisp-tender, 3 to 4 minutes, then immediately transfer with a slotted spoon to a bowl of ice and cold water to stop cooking. Add potatoes to boiling water and simmer, uncovered, until tender, 15 to 20 minutes, then drain in a colander. Halve potatoes while still warm (peel if desired) and toss with 2 tablespoons dressing in a bowl, then cool.

Prepare grill for cooking. If using a charcoal grill, open vents on bottom of grill, then light charcoal. Charcoal fire is medium-hot when you can hold your hand 5 inches above rack for 3 to 4 seconds. If using a gas grill, preheat burners on high, covered, 10 minutes, then reduce heat to moderately high.