Prepare the chicken by placing it on a clean cutting board and cutting it into even bite size pieces. Pat the pieces dry with a paper towel so they will brown well in the pan. Season the chicken with salt pepper paprika and about half of the dried herbs. Toss lightly so every piece is coated.
Chop the onion finely. Mince the garlic. Slice bell peppers into thin strips. Trim broccoli into small florets. Halve the cherry tomatoes or leave them whole if very small. Place the vegetables in a bowl near the stove so they are ready to use.
Start cooking the rice or pasta according to the package directions so it is ready by the time the sauce is done. Keep it warm on low heat once cooked.
Set a large skillet on medium high heat and allow it to warm. Add one tablespoon of olive oil. When the oil looks hot and moves easily across the surface add the seasoned chicken in a single layer.
Cook the chicken without moving it for about four to five minutes until the underside turns golden. Turn the pieces and cook for another three to four minutes until the outside is well browned and the inside is almost cooked through. Transfer the chicken to a plate and set it aside.
Lower the heat to medium. Add the remaining olive oil and the butter to the same skillet. When the butter has melted add the chopped onion. Cook for three to four minutes while stirring often until the onion becomes soft and light gold.
Add the minced garlic. Stir for about half a minute until fragrant. Add the mixed vegetables and a small pinch of salt and pepper. Cook for five to seven minutes stirring from time to time until the vegetables turn bright and begin to soften while staying slightly firm.
Pour the chicken broth into the skillet and use a wooden spoon to scrape any browned bits from the base of the pan. Let the liquid simmer for two to three minutes so the flavor concentrates a little.
Reduce the heat to medium low. Slowly pour in the heavy cream while stirring gently so it blends with the broth. Add the remaining dried herbs. Let the sauce simmer gently for about five minutes until it thickens slightly and coats the back of a spoon.
Return the browned chicken together with any juices on the plate to the skillet. Stir so the pieces are covered in the creamy garlic sauce and mixed with the vegetables. Simmer everything on low heat for another five to seven minutes until the chicken is fully cooked and very tender.
Sprinkle the grated cheese into the skillet and stir until it melts into the sauce. Taste and add more salt or pepper if needed. Turn off the heat and scatter the chopped parsley over the top.
To serve spoon a portion of hot rice or pasta into each bowl or plate. Ladle the creamy garlic chicken and vegetables over the base so each serving has plenty of sauce. Serve at once while hot.