To make pesto, place ingredients in a mini blender or food processor in the order listed and process until almost smooth.

Heat remaining 2 tablespoons of oil in a heavy skillet over medium-high heat. When shimmering hot, add chicken pieces and season well with salt and pepper. Cook undisturbed until browned on the bottom and easily released from pan. Flip and continue cooking until no longer pink inside. Transfer cooked chicken to a plate.

Add vegetables to the same skillet (starting with the ones that require longer cooking time - like cauliflower - giving them a couple of minutes before adding any quicker ones like asparagus). When vegetables start to brown in spots, add a splash of water and stir to deglaze the pan and steam them a bit.  Cook until crisp-tender and then remove from heat.

Cook pasta in a pot of well-salted water for about 6 minutes (or according to manufacturer's directions). Reserve 1/2 cup cooking water before draining. Return drained pasta to the cooking pot along with reserved chicken, vegetables and pesto.