Fill a large pot with water and bring to a rolling boil; while the water heats, prepare all ingredients (chop vegetables, mince garlic, pound and chop chicken, etc.).
Make an ice bath: fill a large bowl with cold water and ice and set a colander or fine-mesh sieve inside the bowl (or use your pasta pot’s drain insert).
In a small bowl, whisk together the spices: 1½ tsp chipotle chili powder, 1 tsp ground cumin, 1 tsp smoked paprika, 1 tsp onion powder, 1 tsp garlic powder, 1 tsp salt, and ¼ tsp pepper. Measure out 1½ tablespoons of this spice mix and set it aside to season the chicken; leave the remaining spice mix for the sauce.
Season the chopped chicken: pat the 2 medium chicken breasts pieces dry with paper towels, then toss them with the reserved 1½ tablespoons spice mix; set aside.
When the pot of water is boiling, generously salt the water. Add the 1 cup asparagus (cut into 1-inch pieces) and blanch for 2–3 minutes until tender-crisp. Use a slotted spoon, fine-mesh sieve, or drain insert to transfer the asparagus immediately to the ice bath to stop cooking. Set the asparagus aside to drain.
Return the pot to a full boil (if needed) and add the 1 pound penne. Cook until just al dente according to package directions. Before draining, reserve ½ cup of the hot pasta cooking water. Drain the pasta (do not rinse) and toss with a light drizzle of olive oil; set aside.
Heat 2 tablespoons olive oil in a large skillet, enameled braiser, or Dutch oven over medium-high heat until hot. Add the seasoned chicken in a single layer and sear 2–3 minutes without moving, then flip and cook another 2–3 minutes, or until cooked through.
Stir in 2 tablespoons honey and 1 tablespoon lime juice to the cooked chicken in the pan and cook just until the chicken is evenly glazed. Transfer the chicken and any glaze to a plate and set aside. Wipe the pan clean.
In the same pan, melt 2 tablespoons unsalted butter with 2 tablespoons olive oil over medium-high heat. Add 1 chopped yellow onion and sauté about 4 minutes until softened.
Add the thinly sliced bell peppers and the remaining spice mix; cook 2 minutes. Add 4–6 cloves minced garlic and cook about 30 seconds, until fragrant.
Sprinkle in ¼ cup flour and cook, stirring, for 1 minute. Reduce heat to low and slowly whisk in 2½ cups low-sodium chicken broth until smooth, then whisk in 1½ cups half-and-half. Stir in 1½ teaspoons chicken bouillon (granulated/crushed/base) and ½ teaspoon dried oregano. Increase heat to medium-high and simmer, stirring often, until the sauce thickens.
Reduce heat to low. Working in batches, stir in 1 cup freshly shredded sharp cheddar until melted, then stir in ½ cup freshly grated Parmesan until melted. If needed, cook 1–2 minutes on low to fully melt the cheeses.
Stir 1 tablespoon lime juice into the sauce. Add the cooked chicken (with any reserved glaze), the drained asparagus, ½ cup frozen petite peas (do not thaw), and the cooked penne. Toss to combine and heat through.
If the sauce is too thick, thin it with the reserved ½ cup pasta water a little at a time until you reach the desired consistency. Taste and adjust seasoning with salt, pepper, and/or additional chipotle chili powder to taste.
Serve garnished with additional freshly grated Parmesan cheese, fresh parsley or cilantro, and a squeeze of lime juice (optional).