Cook the penne in a large pot of salted water until al dente. Reserve 1 cup pasta water, then drain.
Toss the chicken with the chili powder, cumin, smoked paprika, 1/2 teaspoon salt, and black pepper.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Cook the chicken for 5 to 6 minutes until browned and cooked through, then transfer it to a plate.
Add the remaining olive oil, bell peppers, and onion to the skillet. Cook for 6 to 8 minutes until tender and lightly charred. Add the garlic and cook for 30 seconds.
Reduce the heat to medium. Add the dairy free milk and dairy free cream cheese-style spread, stirring until smooth.
Add the pasta, chicken, remaining salt, and 1/4 cup pasta water. Toss until creamy, adding more pasta water as needed.
Stir in the lime juice, garnish with cilantro, and serve hot.