Start by bringing a large pot of salted water to a boil, then cook the pasta according to package directions until al dente, remembering to reserve about ½ cup of the pasta water before draining.
While the pasta cooks, pat the chicken dry and slice it into bite-size pieces or strips, seasoning them well with kosher salt, black pepper, and dried oregano.
In a large pan, heat the olive oil over medium-high until shimmering, then add the chicken and cook, stirring occasionally, for 7 to 8 minutes until golden and cooked through.
Stir in the garlic and sun-dried tomatoes for about 30 seconds, then add the grape tomatoes and artichoke hearts, tossing everything together as you lower the heat to medium-low.
In a small bowl, whisk together the milk, flour, and Parmesan cheese, then pour this mixture into the pan along with the baby spinach.
Add a splash of the reserved pasta water to help the sauce thicken, stirring everything gently.
Finally, toss the cooked pasta into the pan, mix to combine, sprinkle with parsley, and serve hot.