With a freshly washed and sanitized cutting board and knife, slice the fresh beef into thin slices and then again into thin strips. Line up all the strips and dice the meat into as finely ground bits as you can cut. Transfer the chopped raw meat into a large bowl.
Clean the cutting board and knife well and prepare to chop the flavoring ingredients.
Drain 1 tablespoon of capers and finely dice them, add to the fresh meat.
For the two shallots, remove the skin and dice them into small pieces. (Everything should be chopped as small as possible to create classic beef tartare.) Add the shallot to the raw beef.
Next, line up the chives and mince them as fine as possible. Add to the small bowl with everything else.
Now add in the dijon mustard, Worcestershire sauce, and Tabasco hot pepper sauce. (If you don't like spice, just substitute lemon juice.)
Stir well and finely add the olive oil, just enough to bind the ingredients, provide moisture, and get them to hold a good shape for presentation. The desired consistency may vary for different cooks.
Season with salt and pepper. Start with 1 teaspoon salt and add more to taste.
For the Aioli:In a small bowl combine the mayonnaise, lemon juice, pinch of salt. Press the garlic through a garlic press or mince finely and add to the aioli. Stir well and taste for seasoning.
Chill until ready to use. This sauce is best if it is allowed to develop over several hours or overnight.
Notes
Do not keep leftovers for food safety reasons. Consult with your doctor about whether it is safe to enjoy raw or undercooked beef for you and your family.