Preheat oven to 400F (200C). Toss broccoli florets with 1 tablespoon of olive oil and 1/4 cup of Parmesan cheese on a parchment-lined baking sheet. Roast for 18-20 minutes until edges are crispy.
Season chicken strips with oregano, lemon juice, salt, and pepper. Heat 1 tablespoon of olive oil in a large skillet over medium-high heat and sear chicken until golden and cooked through (internal temperature 165F). Remove chicken from skillet and set aside.
Cook fettuccine in a large pot of boiling salted water according to package directions until al dente.
In the same skillet used for the chicken, add the remaining tablespoon of olive oil and butter. Sauté the sliced mushrooms until browned, approximately 5-7 minutes.
Add the minced garlic to the mushrooms and cook for 1 minute until fragrant. Pour in the heavy cream and bring to a gentle simmer.
Whisk the remaining 3/4 cup of Parmesan cheese into the cream until the sauce thickens. Fold in the spinach, artichoke hearts, and fresh basil, stirring until the spinach is wilted.
Return the chicken to the skillet and add the cooked fettuccine. Toss well to coat the pasta in the mushroom basil cream sauce.
Serve the chicken alfredo immediately with the crispy parmesan broccoli on the side.