To make the vinaigrette, whisk the mustard, lemon juice, and vinegar in a bowl until they blend. Add the oils slowly while whisking to create a light emulsion.
Bring a pot of water to a rolling boil. Cut the stem core out of the top of the tomatoes, and cut an X in the bottom. Plunge the tomatoes in the boiling water for 15-20 seconds, then rinse under cold water. The peel can now be removed easily. Slice the tomatoes in half crosswise and remove the seeds and pulp.
Combine the results of the first step with the tomatoes, garlic, thyme, salt and pepper in a food processor or blender. Mix until well blended. Thin with a little vinegar if necessary.
Allow tuna fillets to stand at room temperature for 15 minutes. Season all sides with salt and pepper.
Heat the olive oil in a heavy skillet until almost smoking. Place four tuna blocks at a time in the pan and cook over high heat for about 20 seconds per side, till all sides are lightly browned. Repeat till all are cooked, adding more olive oil if necessary.
Toss the arugula or spring mix with enough vinaigrette to coat, and place in the center of the plate. Place tuna around the salad, and drizzle with more of the vinaigrette.