In a small bowl, whisk together the mustard, vinegar, lemon juice, soy sauce, and pepper. Set aside.
In a large skillet, heat the oil over medium heat. Add the shallots and cook, stirring occasionally, until translucent, 2 to 3 minutes. Add the garlic and cook until fragrant, about 30 seconds.
Add the carrots and cook, stirring constantly, until they are softened but not mushy, about 5 minutes. Transfer the vegetables to a large bowl.
Add the tuna and the dressing to the bowl and mix until thoroughly combined, breaking up the tuna with a awooden spoon. Cool to room temperature or in the refrigerator for about 1 hour to let the flavors meld.
Garnish with shiso, parsley, basil, or mint.