Prepare the ingredients as listed above.
Make iced ginger tea: Bring water to a simmer in a small pot. Remove from heat and steep ginger tea bags for 10 minutes. Sweeten with sugar or honey to taste. Remove tea bags, cool, then refrigerate until ready to serve over ice.
Bring a pot of salted water to a boil.
Grill chicken: Preheat grill or grill pan over medium heat. Drizzle chicken with olive oil and season with salt and pepper. Grill on both sides to an internal temperature of 160°F (71°C). Let it rest, then slice before using.
Prepare sauce: heat olive oil in a large skillet over medium heat. Add shallot and sauté until soft, about 2–3 minutes. Stir in butter until melted. Stir in flour until combined. Add lemon juice and broth. Bring to a simmer until the sauce thickens to a creamy consistency. Season with salt and pepper.
Cook pasta according to package instructions until al dente.
Combine pasta and sauce: Toss the pasta with the sauce to coat. Sprinkle in Parmesan cheese until combined.
Grill zucchini: Toss zucchini with olive oil, oregano, salt, and pepper. Grill until tender and browned, about 4 minutes per side. Season with salt to taste.
Serve the pasta with grilled chicken, grilled zucchini, watermelon slices, and iced ginger tea.