Bring a large pot of water to a boil, salt generously, and cook the spaghetti until al dente according to package directions; reserve 1/2 cup pasta water and 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 and cook, stirring, until fragrant and the kale is wilted and tender, about 2 minutes.
Sprinkle the flour over the kale mixture, stir, and cook 1 minute to remove the raw flour taste.
Reduce heat to medium-low and whisk in the milk until smooth to prevent lumps.
Stir in the chicken bouillon paste, basil, thyme, oregano, red pepper flakes, salt, and black pepper until well combined.
Add the cooked shredded chicken, chopped artichoke hearts, and 1/2 cup grated Parmesan; stir and cook about 3 minutes until the sauce thickens and the chicken is heated through. If sauce is too thick, add reserved pasta water a few tablespoons at a time to reach desired consistency.
Toss the hot cooked spaghetti with the sauce until evenly coated. Serve topped with additional Parmesan if desired.
