Cook pasta in boiling water for 15-20 minutes. When done, drain and set it aside.
Using paper towel, dry chicken pieces. In a small bowl, add 3 tbsp of flour and coat chicken evenly.
Turn on oven to 425°. Heat large skillet over medium heat and add olive oil and butter. When olive oil starts to sizzle, add onions and sauté until soft. Add chicken pieces and cook for 2-3 minutes.
Add ham, mushrooms, thyme leaves, wine and 2 tbsp flour to the skillet and stir to combine.
Next, add milk or half and half, parmesan cheese, ½ cup shredded cheese and cooked pasta to the skillet. Mix all the ingredients well then turn off heat. When the skillet has cooled off after few minutes, add spinach to the skillet and combine with the pasta mixture.
Transfer pasta mixture in individual gratin dish, sprinkle shredded cheese and place boiled egg wedges on top. Place gratin dishes on baking sheet and bake pasta for 10 minutes or until cheese turns golden brown.