Fill a 6- to 8-quart pan halfway with water. Add vinegar and peppercorns; bring to a boil over high heat.
Meanwhile, slice about 1 inch off tops of artichokes; discard tips. Trim stems flush with bottoms. Pull off and discard small leaves from bottoms. With scissors, cut thorny tips from remaining outer leaves.
Add artichokes to water and simmer, covered, until bottoms pierce easily, 30 to 35 minutes; drain.
While artichokes cook, make lemonnaise. In a blender or food processor (a blender produces the best results), whirl tofu, lemon juice, oil, and mustard until smooth. Season with salt and pepper. (If making ahead, chill airtight up to 1 day; stir before using.)
Serve artichokes with sauce for dipping.
Varying your dunk sauce: For variations on lemmonaise (step 4 above), add ingredients to the basic recipe and whirl in a blender or food processor until smooth.
Aioli: Add 1 clove minced garlic.
Caper-anchovy sauce: Add 2 teaspoons drained capers and 1 1/2 teaspoons anchovy paste.
Chili-cilantro sauce: Instead of lemon juice, use 4 teaspoons lime juice. Add 1/2 to 1 stemmed fresh serrano chili and 1/3 cup packed fresh cilantro.
Dried-tomato sauce: Add 1/4 cup dried tomato halves (not oil-packed).
Green sauce: Add 1 cup each lightly packed spinach leaves and parsley, and 1/2 cup chopped green onions.
Madeira sauce: Add 2 tablespoons each madeira and minced chives.
Orange-coriander sauce: Use only 1 tablespoon lemon juice. Add 4 teaspoons orange juice and 1/2 teaspoon each ground coriander and grated orange peel.
Tamari-sesame sauce: Substitute Asian (toasted) sesame oil for olive oil. Add 1 1/2 teaspoons tamari.
Nutritional analysis per serving with lemonnaise.