Bring a large pot of water to a rolling boil for the pasta; generously salt the boiling water. While it heats, prep the chicken (pounded and chopped), onion (chopped), bell peppers (thinly sliced), asparagus (1" pieces), and mince the garlic. Prepare a bowl of ice water for the asparagus.
In a small bowl, whisk together the spices: 1 ½ teaspoon chipotle chili pepper, 1 teaspoon each ground cumin, smoked paprika, onion powder, garlic powder, and salt, and 1/4 teaspoon pepper. Remove 1 ½ tablespoons of this spice mix and set it aside for the chicken; leave the remainder for the sauce.
Pat the chopped chicken dry with paper towels. In a bowl or on the cutting board, toss the chicken pieces with the reserved 1 ½ tablespoons spice mix until evenly coated. Set the chicken aside.
When the water is boiling, add the asparagus and cook 2–3 minutes until tender-crisp. Use a slotted spoon or drain insert to transfer the asparagus immediately to the ice water to stop cooking. Leave the ice bath while you cook the pasta.
Return the pot to a boil (if necessary) and add the penne. Cook until just al dente according to package directions. Before draining, reserve ½ cup of the pasta cooking water. Drain the pasta (do not rinse) and toss briefly with a small drizzle of olive oil to prevent sticking; set aside.
Heat 2 tablespoons olive oil in a large skillet or braiser over medium-high heat until shimmering. Add the seasoned chicken in a single layer and sear 2–3 minutes per side, until cooked through and lightly browned. Stir in 2 tablespoons honey and 1 tablespoon lime juice, coating the chicken with the glaze. Transfer the glazed chicken and any pan juices to a plate. Wipe the pan clean to remove remaining honey residue.
In the same pan, melt 2 tablespoons unsalted butter with 2 tablespoons olive oil over medium-high heat. Add the chopped yellow onion and sauté about 4 minutes until softened. Add the sliced bell peppers and the remaining spice mix (from step 2) and cook 2 minutes. Add the minced garlic and sauté 30 seconds more.
Sprinkle 1/4 cup flour over the vegetables and cook, stirring, for 1 minute. Reduce heat to low and slowly whisk in 2 1/2 cups low-sodium chicken broth until smooth, then whisk in 1 1/2 cups half-and-half (or your chosen alternative from the ingredient list). Stir in 1 1/2 teaspoons chicken bouillon and 1/2 teaspoon dried oregano. Increase heat to medium-high and simmer, stirring often, until the sauce thickens, about 3–5 minutes.
Reduce heat to low. Working in batches, stir in 1 cup freshly shredded sharp cheddar until melted, then stir in 1/2 cup freshly grated Parmesan until melted and the sauce is smooth. If needed, cook 1–2 minutes on low to fully melt the cheese.
Stir in 1 tablespoon lime juice, then add the cooked chicken (with any collected glaze), the drained asparagus, and 1/2 cup frozen petite peas (do not thaw). Gently fold in the cooked penne. If the sauce is too thick, add the reserved ½ cup pasta water a little at a time until you reach the desired consistency.
Taste and adjust seasoning with additional salt, pepper, and/or a pinch more chipotle chili pepper if you want more heat.
Serve topped with extra freshly grated Parmesan, chopped fresh parsley or cilantro, and additional lime juice if desired.