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, vinegar, salt, and red pepper flakes in a blender until smooth, about 2 minutes.
Transfer to a heavy 12-inch 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. Serve immediately.
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