Chop the cauliflower by hand into half-inch to 1-inch chunks. Dice the bell pepper into small pieces. Place the bell pepper and cauliflower in a bowl, cover with 2 tsp. of olive oil, and season with a bit of salt and pepper. Toss to coat evenly.
Mince the garlic, ginger, and shallots and set aside.
Remove the lettuce leaves from the head of lettuce and wash them. You will need two pieces of lettuce per taco for more stability (so you get eight tacos total).
Heat a large sauté pan over medium high heat.
Chop the chicken breasts into 1-inch chunks and season with a bit of salt and pepper. Coat the chicken breasts in 2 tsp. olive oil and sauté for about 5-7 minutes, or until they are cooked through, stirring occasionally.
Remove the chicken and set aside in a clean bowl.
Sauté the cauliflower and bell pepper mixture for about 5-7 minutes, stirring frequently.
Add the shallot and sauté for about 30 seconds to 1 minute, then cover with a lid for about 1-2 minutes or until the veggies are softened but still have a bit of texture.
Add the garlic and ginger and sauté for no more than 1 minute, stirring frequently.
Add the soy sauce, chicken broth, and cooked chicken breasts. Stir constantly until the sauce is mostly absorbed into the vegetables, about two minutes.
Top with a squeeze of lime, transfer to a bowl, and set aside.
If adding an egg, wipe out the sauté pan and add a touch of oil. Spread it with a pastry brush or paper towel to keep the eggs from sticking, then fry up to four eggs at a time over medium heat, depending on how big your pan is. Cover and cook the eggs sunny-side up.
Add about ¾ cup of the stir fry mixture to each lettuce wrap along with some shredded carrots, sesame seeds, and cilantro leaves, then top each one with an egg. Drizzle with hot sauce if you like it spicy and enjoy!