Step 1

For the vinaigrette: Combine the oil, pickle brine, vinegar, mustard and 1 tablespoon of the honey in a blender, mini food processor or in a lidded jar you can shake. Season lightly with salt and pepper. Blend or seal and shake to form a creamy, emulsified vinaigrette. This should take a minute or less. Taste and add more brine, vinegar or honey, a teaspoon or two at a time, as needed. The yield is 3/4 cup.

Step 2

For the salad: Put the potatoes in a pot with just enough water to cover them. Bring to a boil over medium-high heat, add a large pinch of salt and then reduce the heat to medium or medium-low, so the water bubbles gently. Cook for about 15 minutes, until tender but still somewhat firm. Drain, rinse under cool water for a minute, then drain again.

Step 3

Toss the still-warm potatoes with the chopped cornichons and dill in a large bowl. Stir in 1/2 cup of the vinaigrette; let the salad sit for a few minutes, then taste. Add more of the vinaigrette and season with salt and pepper, until you are happy with the flavor.

Step 4

Serve right away, or cover and refrigerate for at least 1 hour (to chill thoroughly) and up to 2 days.