If chicken pieces are large, cut them into smaller serving-size pieces.
Heat 1 tablespoon each of the butter and oil in a large, heavy skillet over medium-high heat. Add as many pieces of chicken as can comfortably fit in the skillet without overcrowding. Cook for 3 to 4 minutes on each side, until golden brown and no longer pink inside, seasoning each side of the chicken with all-purpose seasoning and pepper to taste as it cooks. Transfer chicken to a platter or large rimmed serving dish and cover with foil to keep warm. Repeat with remaining butter, oil, chicken and seasoning.
Mix cornstarch with water in small bowl and set aside.
Add garlic to the skillet and cook, stirring for just a minute or two until softened and fragrant, being careful not to burn. Add the dry sherry or white wine to the skillet. Using a whisk, scrape the brown bits from the bottom of the skillet and let the sherry simmer for a minute or two. Add the broth, Dijon mustard, and lemon juice and whisk again to combine. Allow the sauce to simmer for several minutes to reduce slightly. Add the cream and simmer for another 2 to 3 minutes, stirring constantly. Add cornstarch/water slurry to skillet and stir until slightly thickened. Add chicken back to pan, spooning sauce over chicken and sprinkle with chives.
Toss prepared pasta with a little olive oil and sprinkle with Parmesan cheese. Serve chicken over prepared pasta with sauce drizzled over the top.
Note about scaling down: If you scale this down and use less chicken, I would not recommend scaling down the sauce ingredients. A little extra sauce is never a bad thing.