Heat frying pan and your choice of cooking oil on medium. Cut bacon into small pieces and add to hot frying pan. Fry bacon til crispy then remove from pan, leaving rendered fat in pan, and set aside.
Add dairy-free spread to oil in pan and wait for it to melt. Sprinkle flour over melted oil and whisk together. It should make a thick paste without any clumps. If it's a bit dry just add more oil and whisk together some more.
When the roux is nicely golden, slowly pour the milk in while continuing to whisk. Keep whisking until they come together and there are no clumps.
Chop brie into small chunks and add to sauce. Slowly stir to melt the brie into the sauce. Turn heat to low and let sauce cook down, stirring occasionally. Add more milk occasionally if your sauce has thickened more than you want.
Bring a pot of salted water to boil then add spaghetti. Cook a few minutes shy of the directions, about 5-6 minutes. Use a mug to save some pasta water, then drain spaghetti and add directly to the cheese sauce. Toss together with tongs.
Add peas and bacon, along with a bit of pasta water if the sauce needs loosened. Toss gently until everything is mixed completely, the peas are hot, and the pasta is cooked through (roughly 2-3 more minutes). Salt and pepper to taste.
Dish up into two large pasta bowls, crack some more black pepper onto pasta, and sprinkle with some chopped parsley if you're feeling fancy.