Make the bread. You'll want to make the "sandwich roll" version of the low carb bread for this recipe. Once the bread has cooled, use a bread knife to slice it in half lengthwise, so you have 2 slices of bread per sandwich. Alternatively, you can skip the bread and turn these into bowls, or use a hollowed-out cucumber.
Pickle the veggies. In a small saucepan, bring the vinegar, water, and erythritol to a boil until the erythritol dissolves completely. Place the sliced carrots and onions in a heat-safe bowl, and pour the vinegar over the top. Secure a lid over the veggies and set aside for at least 30 minutes.
Bake the chicken. Preheat oven to 425 F. Place chicken in a bowl with oil and toss to coat. sprinkle with salt and pepper, and toss again. Place thighs in a 9x13 baking dish, and cook in the preheated oven until they reach an internal temp of 165 F--about 25 minutes. Allow chicken to rest for 10 minutes, then cut into bite-sized pieces.
Assemble. Combine the mayonnaise and soy sauce together in a small bowl. Brush half the sandwich roll with the soy sauce mayonnaise combo. Brush the other half with pate (if using). Place a layer of cucumbers over the mayonnaise, then sliced chicken, then pickled veggies, cilantro, and jalapenos. Place the other half of your bread on top and dig in!