In a skillet, heat 1 tbsp. l. olive oil and fry the bacon until crispy. Transfer to paper towels, then break into small pieces.
Peel and finely chop the shallot. Put the onion in the pan where the bacon was fried, add vinegar and honey and heat over medium heat for 3 minutes. Remove the pan from the heat and add the olive oil, salt and pepper and beat the mixture well with a whisk.
Navarte lettuce, cut the eggs into slices. Place lettuce and eggs on a platter, drizzle with dressing and sprinkle with basil. Sprinkle with bacon before serving.