Melt the butter in a small frypan, and cook the mushrooms & garlic for 2 minutes. Remove from heat.
Cook the pasta until just al dente in salted water. Drain, and return to the pan.
While the pasta is cooking, beat the eggs, parmesan and cream together in a bowl until well combined. Stir the ham and mushrooms through the mixture. Pour the sauce over the hot pasta and toss gently to combine.
Return th epan to very low heat and cook for 1 minute. Add pepper to taste.