Preheat the oven to 350 degrees F. Boil the pasta in a very generous amount of water until just tender (see package for suggested cooking time).
While the pasta cooks, lightly brush and grease an 8" x 8" baking dish with olive oil. To make sauce, place the soy beverage and cornstarch in a medium pot and whisk to combine. Mix in the oregano, paprika and garlic. Bring mixture to simmer over medium to medium-high heat, whisking regularly. Simmer 1 minute, just until sauce is lightly thickened. Remove from the heat and mix in three-quarters of the cheddar-style shreds. Season the sauce with salt and pepper.
When the pasta is cooked, drain well, rinse lightly with cold water, and then drain well again. Add pasta, tuna and peas to the sauce. Spoon the mixture into the baking dish. Sprinkle with the remaining cheddar-style shreds. Bake 20 minutes, or until pasta is piping hot. Sprinkle with green onion and serve.
Note: Daiya cheddar-style shreds is a dairy-free product sold alongside products such as tofu. Gluten-free pasta, made with ingredients such as rice bran, is available in the aisle where other dried pastas are sold.
This recipe yields quite a thick, Mac & Cheese-style, end product. If you prefer saucier pasta, simply reduce the amount of cheddar-style shreds you add to the sauce.