To make the vinaigrette, combine the mustard, vinegar, oil, and tobiko in a small bowl. Season with the salt and pepper and whisk lightly.
In a small chilled bowl, whip the cream until stiff peaks form. Reserve.
Fill a large bowl with ice. Place a medium bowl in the ice and add the tuna, Tabasco sauce, chopped chives, and olive oil. Season with salt and pepper to taste and mix lightly.
Spray the insides of four 1- to 1 1/2-inch ring molds, or tuna cans with tops and bottoms removed, with nonstick cooking spray. Layer the tuna mixture and caviars in the molds as follows: one-eighth of the tuna, one-fourth of the tobiko, one-eighth of the tuna, one-fourth of the osetra. Press down lightly on the parfaits after each layer with the bottom of a Tabasco bottle (it's the perfect size) or the butt end of a whisk. Top the layers with a thin layer of the cream, smooth to cover, and unmold cream side up onto white serving plates. Or use the Tabasco bottle to push the parfaits from the bottom, then carefully lift them onto a plate. Garnish each portion with 2 chives. Drizzle the vinaigrette around and serve with demitasse spoons.