Make iced ginger tea: Bring water to a simmer in a small pot. Remove from heat, steep ginger tea bags for 10 minutes, then sweeten with sugar or honey. Let cool and refrigerate. Serve over ice.
Cook pasta: Boil pasta according to package directions. Drain and set aside.
Cook chicken: Season chicken with paprika, Italian seasoning, salt, and pepper. Heat olive oil in a skillet over medium-high heat. Cook chicken on both sides until golden and it reaches 160°F (71°C). Rest, then slice thinly.
Make sauce: In the same skillet, melt butter. Sauté garlic for 30 seconds. Stir in flour to form a paste. Gradually whisk in broth, cream, and Parmesan until smooth. Add sun-dried tomatoes and simmer until sauce thickens. Adjust seasoning as needed. Toss in pasta, then top with sliced chicken. Garnish with basil and extra Parmesan.
Prepare spring rolls: Soften rice paper in warm water. Lay flat and layer with lettuce, carrot, cucumber, jalapeño, scallions, mint, and cilantro. Roll tightly and set aside.
Make peanut sauce: Mix peanut butter, rice vinegar, soy sauce, honey, sesame oil, and garlic. Gradually whisk in water until smooth and dippable.
Serve the chicken pasta with spring rolls, peanut sauce, and iced ginger tea.