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Step 1
Bring a large pot of water to a boil. Add a small handful of salt and the pasta. Cook according to package directions (approximately 6-10 minutes) and then drain the pasta. Stir together the cream, thyme, 1/4 teaspoon salt and 1/8 teaspoon pepper. Set the cream mixture aside.
Step 2
While the pasta is cooking, heat a large skillet over medium high heat. Add the broccoli and 2 tablespoons of water and cover with lid. Allow the broccoli steam for 1-2 minutes, until bright green and almost tender. Remove the lid and add the peppers and mushrooms. Cook, stirring occasionally, for 3-4 minutes, letting the vegetables brown a bit between tossing each time. Sprinkle with the remaining salt and pepper. When the vegetables are cooked, but still crisp, remove them to a bowl.
Step 3
Add the ham to the hot skillet and allow it to brown for a minute or so before stirring. When the ham pieces are hot and lightly browned, add the cream to the skillet. Let it simmer and slightly thicken for 1-2 minutes, until it coats the ham pieces. Add the vegetables, toss to coat and then stir in the pasta. Let the sauce cook for another 2-3 minutes as needed, to thoroughly coat the pasta. (If the pasta is too dry, add a small splash of milk until it reaches the desired consistency.)
Step 4
Grate cheese over the top of the pasta and toss to combine and melt the cheese. Serve with additional cheese sprinkled on top, if desired. Enjoy!