To prepare the marinade, whisk together all ingredients except the olive oil in a medium bowl. Once the mixture is well blended, add the olive oil in a thin stream, whisking until emulsified.
Add the sliced duck or goose to the marinade, toss to coat evenly, cover, and refrigerate for 6 to 12 hours, turning occasionally.
To prepare the mayonnaise, place the egg yolks, mustard, lemon juice, and garlic in a blender or food processor. Pulse to blend. With the motor running on low speed, add the vegetable oil in a thin stream until the mayonnaise is creamy. Add the herbs and season the mayo to taste with salt and pepper. Store in the refrigerator for up to 2 weeks.
Remove the sliced breast fillets from the marinade and pat dry. Cook in a hot, lightly oiled skillet for 2 to 3 minutes or until desired doneness.
To serve, spread a layer of mayonnaise over each flour tortilla. Add the cooked breast fillets, lettuce, tomato, and cheese. Fold over the bottom flap and roll tightly.