Pasta water: Start the water boiling for your pasta in a large pot, meanwhile season the chicken and prep the veggies. Spice Mix: In a small bowl, whisk the spices together. Remove 1 1/2 tablespoons to use on the chicken (the rest is for the pasta sauce).
Season chicken: While the chopped chicken is still on the cutting board, pat dry with paper towels, then toss with the 1 1/2 tablespoon spice mix; set aside.
Cook asparagus: Prepare a large bowl of ice water and place a colander inside (skip colander if you have a pasta pot with drain insert). Season the boiling pasta water generously with salt. Add the asparagus and boil for 2-3 minutes or until tender crisp. Use a fine mesh sieve (or drain insert) to transfer the asparagus to the colander in the ice bath to prevent it from continuing to cook. Cook pasta: Cook pasta in the boiling water just until al dente. Reserve ½ cup pasta water before draining. Drain, rinse and toss pasta with a drizzle of olive oil; set aside.
Cook chicken: Heat 2 tablespoons olive oil in an enameled cast iron braiser or Dutch oven over medium-high heat. Once smoking, add chicken in a single layer. Sear chicken for 2-3 minutes, then flip over. Continue to cook for an additional 2-3 minutes, or just until cooked through. Stir in 2 tablespoon honey and 1 tablespoon lime juice, until evenly coated. Transfer to a plate including all of the yummy glaze (use a spatula to get it all). Wipe the pan clean (so the residual honey doesn’t burn). Sauté onions and peppers: To the now empty pan, melt 2 tablespoons butter in 2 tablespoons olive oil over medium-high heat. Add onions and sauté for 4 minutes. Add bell peppers and remaining spice mix and cook for 2 minutes. Add garlic, and sauté for 30 seconds. Make sauce: Sprinkle in the flour and cook for 1 additional minute. Reduce heat to low, then slowly whisk in the chicken broth, followed by the half and half. Stir in the chicken bouillon and oregano. Increase heat to medium-high and bring the sauce to a simmer until thickened, stirring often.
Add cheeses: Reduce heat to low. Working in batches, stir in the cheddar until melted, followed by Parmesan cheese until melted. You may need to cook for 1-2 minutes on low for the cheeses to completely melt. Combine and season: Stir in the lime juice, chicken, asparagus, and peas, followed by the pasta. Season with salt, pepper and/or chipotle chili pepper to taste. If you would like to thin the sauce (optional), add some reserved pasta water a little at a time. Garnish with freshly grated Parmesan cheese, fresh parsley or cilantro and lime juice (optional).