1. Cook the pasta in salted water until soft. In a frying pan, heat the vegetable oil, brown the garlic. Add the broccoli florets, a little salt and cook over medium heat until broccoli begin myagchet. Heat oven to 190 degrees, grease a baking dish with butter.
2. In a frying pan fry the shallots in butter, add flour and a pinch of salt. Keep stirring on the fire for 2-3 minutes. Gradually pour in the chicken broth and cook over medium-high heat. Pour in the milk, bring to a boil. Stir constantly until thickened (6-7 minutes). Remove from heat and sprinkle in the grated cheddar and parmesan. Stir to melt the cheese.
3. Mix the chopped chicken, pasta, broccoli with sauce until smooth. Pour this mixture into the prepared dish. Sprinkle with grated Parmesan cheese and breadcrumbs. Bake for 20-25 minutes, then put on the broiler for a few minutes to become more crispy crackers and podzolotilis.