Bring a large pot of salted water to a rolling boil.
In a 10-inch skillet over medium-high heat, heat the olive oil until it shimmers.
Add the mushrooms and a pinch and salt and saute, stirring occasionally, until pale brown, about 5 minutes. Add the spring onions and cook, stirring occasionally, until warmed through, about 1 minute. Stir in the red bell pepper flakes, and remove the pan from the heat.
Add the fettuccine to the boiling water and cook approximately halfway, until malleable but still quite firm, 4 - 5 minutes.
Add the broccoli snap or snow peas, and asparagus to the pasta pot. Cooking until the fettuccine is al dente and the vegetables are bright green and tender, 4 to 6 minutes.
Stir in the frozen peas and let them cook for 20 seconds.
Reserve 1/4 cup of pasta water. Drain the pasta and vegetables, but do not shake them to dry further. Immediately return them back to the pot.
Return the skillet with the mushrooms and spring onions to medium heat.
Stir in the cream, followed by the cheese, letting it melt.
Add the mushroom and cream mixture to the pasta and vegetables, along with the cherry tomatoes and reserved pasta water, and cook, stirring, until the sauce just barely coats everything.
Taste the Pasta Primavera and season with more salt, if desired. Add more cream and cheese, if you like.
Divide among 4 plates or shallow bowls, top with basil and black pepper, and serve.