Bring a large pot of salted water to a boil and cook the chickpea pasta according to package instructions; drain and set aside.
Pat the chicken breasts dry and evenly coat both sides with the Cajun blackening seasoning.
Heat a large cast-iron or heavy skillet over medium-high heat and melt 2 tablespoons of the butter until foaming.
Add the seasoned chicken to the hot skillet and cook about 5 minutes per side, until cooked through and an instant-read thermometer reads 165°F (74°C); remove from heat and let rest 5 minutes.
Slice the rested chicken into strips and set aside.
Wipe out the skillet or use a second clean skillet and melt the remaining 2 tablespoons of butter over medium heat.
Add the minced garlic and shallot and cook, stirring, about 1 minute until fragrant; stir in the dried mixed herbs and season with a dash of salt and pepper.
Whisk together the milk, water, and cornstarch until smooth, then pour into the skillet and bring to a gentle simmer over low heat, stirring until the sauce thickens, about 3–5 minutes.
Stir in the grated Parmesan until melted and the sauce is smooth.
Add the cooked pasta and sliced chicken to the sauce and gently toss to combine and coat everything evenly.
Transfer to a serving dish, sprinkle with chopped parsley, and serve immediately.
