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In a heavy bottom dutch oven, brown off the kielbasa and ham. Some fat will render out, and the meats should get a little color on them. Remove from the pot with a slotted spoon and place in a bowl.
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Add a little oil if the pan is dry, and brown off your chicken. You want to make sure your chicken pieces are mostly cooked through at this point. Remove the chicken to the bowl with the kielbasa & ham.
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If the pan is dry, add a little oil. Add all of your vegetables, and give them a stir. You will cook the veggies for about 8 minutes until they are tender. One trick for this is to add a splash of your chicken stock, and then cover the pot with a lid so that the veggies steam. I have found this goes much faster than sautéing them or simmering them when I’m making soups and 1 pot meals in a hurry.
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Once the veggies are soft, add all of the spices. Cook for another minute so they are warmed through and start to release some of their goodness.
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Dump in the can of tomatoes and chicken broth, and add the chicken, kielbasa, and ham back to the pot. Bring it up to a simmer and cook for 5 minutes.
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Stir in the brown Minute Rice, and simmer another 5 minutes covered.
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Turn off the heat, and stir in the shrimp. Cover the pot, and let it stand for 6 minutes. The Minute Rice will absorb all of the broth, and the shrimp will be perfectly cooked.