In a medium bowl, whisk together 2 tablespoons of the black vinegar, the soy sauce, 1 tablespoon of the toasted sesame oil, the granulated sugar, 2 cloves of the garlic, the ginger, the black pepper, and the ground Szechuan peppercorn, until fully combined.
Reserve 1/2 of the marinade, setting it aside.
Add the steak slices to the remaining marinade in the bowl, tossing until evenly coated.
Let the steak marinate at room temperature for 30 minutes.
Drain the steak slices and pat them dry with paper towels.
In a large bowl, toss together the cornstarch and the marinated beef slices, shaking off any excess cornstarch.
In a large skillet over medium-high heat, add 2 tablespoons of the peanut oil.
Add the steak slices to the skillet in a single layer, working in batches as needed.
Cook the steak slices until they are seared, about 1-2 minutes per side.
Transfer the steak slices to a plate. It is okay for them to not be fully cooked yet.
Return the skillet to medium heat.
Add the remaining peanut oil.
Add the bean paste, the dried chiles, the whole peppercorns, the remaining garlic, 3 of the green onions, and the salt.
Stir and cook until fragrant, about 1-2 minutes.
Add in the chile oil, the bell peppers, and the carrots and cook, stirring occasionally, until slightly softened, about 4 minutes.
Add the broth and cook, stirring occasionally, until the vegetables are tender, about 3-4 minutes.
Add the hoisin, the sambal oelek, and the reserved marinade, stirring until combined.
Bring the hoisin mixture to a simmer.
Add the seared steak slices and toss until evenly coated.
Cook, stirring until the sauce thickens and the steak slices are fully cooked through at a minimum of 135 degrees F internally for medium-rare, about 2-3 minutes.
Transfer the skillet from the heat.
Stir in the remaining sesame oil and the remaining black vinegar.
Garnish with the sesame seeds and the extra green onions.
Serve.