Bring a large pot of salted water to the boil. Add the spaghetti and cook according to packet instructions.
Meanwhile, put the cream and garlic in a small saucepan and bring to a simmer. Add the smoked cheddar and allow to melt over a low heat. You may need to stir it vigorously to make a smooth mixture. Remove from the heat and allow to cool slightly.
Add the beaten egg to the cheese sauce a little at a time, stirring constantly until each addition is smoothly incorporated. (If there are a few lumps of cheese, it really doesn't matter.) Season with freshly ground black pepper.
When cooked, drain the spaghetti in a large colander. Return the spaghetti pan to the heat and add the spinach leaves. Stir until the spinach softens, adding a splash of water if it begins to stick. Stir the spaghetti in to the spinach.
Pour the cheese sauce over the spaghetti and spinach. Add the sun-dried tomatoes and parsley. Toss everything together until the spaghetti is completely coated. Serve immediately, preferably with a crisp green salad and a grating of Parmesan.