Bring a large pot of salted water to a boil and cook the whole wheat spaghetti until al dente according to package directions; reserve about 1/2 cup pasta water, then drain.
While the pasta cooks, heat the butter and olive oil in a large skillet over medium heat until butter melts.
Add the minced garlic and chopped baby kale to the skillet; cook, stirring, until fragrant and the kale is tender, about 2 minutes.
Sprinkle the flour over the kale and garlic, stir constantly, and cook for 1 minute to remove the raw flour taste.
Slowly whisk in the milk, reduce heat to medium-low, and whisk until smooth to prevent lumps.
Stir in the chicken bouillon paste, basil, thyme, oregano, red pepper flakes, salt, and black pepper. Taste and adjust seasoning as needed.
Add the cooked shredded chicken, chopped artichoke hearts, and grated Parmesan to the sauce; stir to combine.
Simmer the sauce for about 3 minutes, stirring, until it thickens and the chicken is heated through; loosen with reserved pasta water if too thick.
Toss the hot drained pasta with the sauce until well coated, serve topped with additional Parmesan if desired.