In a large pot, bring salted water to a boil. Add the fettuccine and cook over medium heat for around 10-12 minutes, or until al dente. Drain the pasta, reserving a little pasta water if needed later, and toss the fettuccine with a drizzle of olive oil to prevent sticking. Set aside.

In a large pan, melt the butter over medium heat. Add the sliced garlic and cook until fragrant, about 1 minute. Add the sliced button mushrooms and fresh thyme, sautéing until the mushrooms are golden and tender, approximately 5 minutes.

Stir in the diced double smoked ham and cook for another 2 minutes. Then, pour in the thickened cream and bring the mixture to a gentle boil. Stir frequently to ensure the cream doesn’t burn.

Lower the heat and stir in the grated cheddar or parmesan cheese. Continue to stir until the cheese melts and the sauce becomes smooth. Season with salt and pepper to taste.

Add the cooked fettuccine to the pan with the creamy ham and mushroom sauce. Toss everything together, ensuring the pasta is well-coated. If the sauce is too thick, add a splash of the reserved pasta water to loosen it.

Divide the ham and mushroom fettuccine among plates and serve immediately. Garnish with extra cheese or thyme if desired.