Cook the egg noodles in a large pot of salted boiling water according to package directions. Once it's done, drain it and toss it lightly with olive oil to prevent it from sticking. Set it aside. In the same pot, heat the butter over medium heat. Once it's melted, add the onion and cook until it's translucent, just about 3-4 minutes. Stir in the garlic and cook just until fragrant.
Stir in the flour and cook, stirring fairly constantly for a couple more minutes. Then slowly add in the broth and the milk while stirring to fully incorporate everything smoothly. Increase the heat to med-high. Let it come up to a low boil.
Once it's bubbling, lower the heat back down and let it simmer until it's thickened enough to coat the back of a spoon. Then stir in the salt, pepper and peas. Slightly break up the tuna with a fork into large chunks and stir that in as well. Remove from the heat and stir in the cheese until it's melted in, then serve.
