Trim and cut the chicken breasts into roughly 1-inch pieces so they cook evenly.
Heat 1–2 tablespoons olive oil in a Dutch oven over medium heat until shimmering.
Add the chicken pieces, sprinkle with 2 teaspoons garlic powder, 1 teaspoon oregano, and salt and pepper to taste, then cook for about 5 minutes, stirring occasionally.
Add the sun-dried tomatoes and cook until the chicken is mostly cooked through, about 2–3 more minutes.
Stir in the dry orzo and cook, stirring, for 1–2 minutes to lightly toast the pasta.
Pour in 1 quart chicken broth, stir to combine, and bring to a gentle simmer.
Simmer partly covered for 10–15 minutes, stirring occasionally, until the orzo is tender and has absorbed most of the liquid.
Remove from heat and stir in the Boursin cheese and fresh spinach until the cheese melts and the spinach wilts.
Taste and adjust seasoning with additional salt and pepper if needed, then serve topped with grated Parmesan if desired.