Begin to cook pasta in a 6- to 8-quart pot of boiling salted water.
Meanwhile, working quickly, tear toast into pieces and blend with peppers, almonds, garlic, broth, oil, vinegar, salt, and red-pepper flakes in a blender until smooth, about 2 minutes.
Transfer to a 12-inch heavy skillet and bring to a simmer.
When pasta is barely al dente, add peas and continue to cook until peas are just tender, about 2 minutes. Reserve 1/2 cup pasta water, then drain pasta and peas in a colander.
Add pasta and peas to sauce along with cheese (1/4 cup) and toss to combine.
Add some reserved pasta water to thin if necessary.
