Cook the rice according to the directions on the package. Season with salt and pepper. Cover with a lid and set aside. Drain any excess water if needed.
Heat half of the oil in a skillet or non-stick pan over medium-high heat; once the oil is hot, add in the sausage and zucchini, brown them for a few minutes on each side until they become a deep brown color. Remove them from the pan with a slotted spoon, and set aside.
In the same pan, add in the butter, allow it to melt; then add in the sliced onions. Cook until they become a rich golden-brown, about 5-7 minutes. Next, add in the garlic and oregano, season with salt, black pepper, and the paprika. Stir to combine with the onions. Sauté just until the garlic becomes aromatic, about 2 minutes. Add the chicken broth, zucchini and sausage to the pan and bring to a simmer.
Dissolve the cornstarch in an equal amount of water. Slowly add a little at a time to the simmering broth until it reaches a thick and smooth consistency. Stir in the parsely and season with salt and pepper to taste.
Toss with the rice and serve immediately, garnish with parsley.