Bring a large pot of water to a boil for the pasta; season generously with salt.
In a small bowl, whisk together 1 1/2 tsp chipotle/chili powder, 1 tsp cumin, 1 tsp smoked paprika, 1 tsp onion powder, 1 tsp garlic powder, and 1 tsp salt; remove 1 1/2 tablespoons of the mix and set aside for the chicken.
Pat the chopped chicken dry, then toss with the reserved 1 1/2 tablespoons spice mix; set aside.
Add the asparagus to the boiling pasta water and cook 2–3 minutes until tender-crisp, then transfer to an ice bath to stop cooking; reserve a colander or drain insert if available.
Cook the penne in the same boiling water until just al dente; before draining, reserve 1/2 cup pasta cooking water, then drain and toss the pasta with a drizzle of olive oil; set aside.
Heat 2 tablespoons olive oil in a large skillet or braiser over medium-high heat until very hot. Add the spiced chicken in a single layer and sear 2–3 minutes per side until cooked through.
Stir in 2 tablespoons honey and 1 tablespoon lime juice to the chicken, coat evenly, then transfer the glazed chicken and any pan juices to a plate; wipe the pan clean.
In the same pan, melt 2 tablespoons butter with 2 tablespoons olive oil over medium-high heat. Add the chopped onion and sauté about 4 minutes until softened.
Add the sliced bell peppers and the remaining spice mix, cook 2 minutes, then add the minced garlic and sauté 30 seconds until fragrant.
Sprinkle in 1/4 cup flour and cook 1 minute while stirring. Reduce heat to low and slowly whisk in 2 1/2 cups chicken broth, then whisk in 1 1/2 cups half-and-half. Stir in 1 1/2 teaspoons chicken bouillon and 1/2 teaspoon dried oregano.
Increase heat to medium-high and simmer the sauce, stirring often, until it thickens.
Reduce heat to low and, in batches, stir in 1 cup shredded sharp cheddar until melted, then stir in 1/2 cup grated Parmesan until melted, cooking 1–2 minutes if needed for complete melting.
Stir in 1 tablespoon lime juice, the cooked chicken, asparagus, and frozen peas, then add the drained pasta. Toss to combine and adjust seasoning with salt, pepper, and additional chipotle/chili powder to taste. If the sauce is too thick, add reserved pasta water a little at a time to reach desired consistency.
Serve topped with freshly grated Parmesan, chopped fresh parsley or cilantro, and a squeeze of lime if desired.