Step 1

To pickle cucumber: Combine cucumber, vinegar, sugar and 1/2 teaspoon salt in a medium bowl. Let marinate, stirring once or twice, for at least 20 minutes and up to 1 hour. Drain well and pat dry with paper towels.

Step 2

To prepare mayo: Combine egg yolks, basil, vinegar, anchovy to taste, lemon juice, honey and 1/4 teaspoon salt in a blender. Blend until incorporated and green. With the motor running, very slowly drizzle in oil through the feed tube until it's all incorporated.

Step 3

To assemble sandwiches: Slice tomatoes into 1/4-inch-thick slices and season with pepper and salt. Spread each piece of bread with a generous 1 tablespoon of the mayo. Make 4 sandwiches with onion, the pickled cucumber and the tomatoes.