In a large pot, warm the olive oil on medium-high heat. Saute the garlic and brussels sprouts for about five minutes, lowering the temperature as needed.
Stir in 1 tablespoon of lemon juice. Reduce heat to medium-low and cover. Cook until tender, about 10 minutes.
Remove brussels sprouts and garlic from the pan, place in bowl, and set aside.
Heat the vegan butter (or oil) on med-high in the same pot from brussels sprouts. Once melted, stir in the cornstarch with a whisk until combined. Simmer for 1-2 minutes.
Add vegetable broth, non-dairy milk, and season with salt and pepper. Whisk everything together to make sure there are no clumps.
Bring to a boil and add pasta. Stir until all of the pasta is submerged in liquid.
Heat until it reaches a simmer, then reduce the heat to medium cooking for 8-10 minutes, until the spaghetti is cooked through. Stirring to keep noodles in the liquid as the liquid starts to reduce and thicken.
Once the pasta is cooked, add 1 tablespoon of lemon juice and a pinch of salt and pepper.
Add the brussels sprouts and garlic back into the pot, combine them all together, and heat for an additional 1-2 minutes.