1. To make the mayonnaise, put the egg yolk and mustard in a small bowl and whisk together. Slowly whisk in the vegetable oil, a teaspoon at a time at first, to form an emulsion, then continue adding oil in a thin stream, whisking constantly, until the mixture has thickened. Whisk in the lemon juice (this will thin the sauce), then carry on whisking in the olive oil. The mayonnaise should have the texture of softly whipped cream; thin with more lemon juice and a few drops of water if necessary. Season with salt and pepper, the cayenne, and a few drops of red wine vinegar. 

2. To make the salad, bring a small pot of water to a rapid boil. Carefully lower the eggs into the water, reduce the heat, and simmer for 8 to 9 minutes. Drain and immediately place in ice water to cool. Drain and peel. 

3.  Slice the tomatoes about ½ inch thick and place in one layer on a large platter. Season with salt and pepper. Put a spoonful of mayonnaise on each tomato slice. Top with the eggs, quartered or rough-chopped, and sprinkle with the chives. Garnish with the tarragon sprigs.