Prepare the gluten-free spaghetti according to the packet instructions. Drain, reserving 2 tbsp of the pasta water for later, then set aside.
Bring a saucepan of water to the boil and add a tsp of vinegar to it. Crack an egg into a small bowl. Stir the boiling water and immediately add the egg from the bowl, whilst the water is still swirling. Cook for 1-2 minutes or until all of the egg white is clearly cooked (no gooey see through bits around the yolk). Use a slotted spoon to remove from the water and transfer to a plate lined with kitchen paper. Repeat with the remaining 3 eggs. If you're not confident poaching eggs, feel free to use fried eggs instead!
Whilst the pasta is cooking, crack the other 4 eggs into a jug and then add in your grated cheese. Season with salt and pepper. Beat with a fork until combined.
Heat the oil in a large pan over a medium heat. Add your mushrooms and fry for 4-5 minutes or until the mushrooms are browned and a little crispy. Then turn the heat down to low.
Add the spaghetti to the pan and briefly stir so the mushrooms are evenly dispersed.
Next, remove the pan from the heat completely and add in your 2 tbsp of pasta water. Then pour in your egg and cheese mixture.
Make sure you keep moving the egg mixture around and toss the spaghetti to coat it evenly. It’s important the heat isn’t on or your eggs will scramble!
Plate up and serve each with a poached egg on top and optionally, a little fresh rocket scattered on top.