BLT and Poached Egg Salad

INGREDIENTS

• 1 Tbs. Dijon mustard
• 1 tsp. minced shallot
• 1/4 tsp. sugar
• 2 1/2 tsp. kosher salt, plus more, to taste
• Freshly ground pepper, to taste
• 4 Tbs. white wine vinegar
• 3 Tbs. extra-virgin olive oil
• 6 slices thick-cut bacon, coarsely chopped
• 2 cups halved cherry tomatoes or 3 large tomatoes, chopped
• 3 Tbs. fresh basil leaves, torn
• 4 cups torn butter lettuce leaves
• 4 to 6 eggs