In large, heavy skillet or deep heavy soup pot, add olive oil, heat and add 1 sliced garlic clove garlic (or more, to taste). Sauté on low to infuse oil with garlic flavor, do not burn or brown garlic, about 5 minutes.
Add butter and continue to sauté garlic. When garlic is tender and translucent, remove and toss in the raw mushrooms. Brown and caramelize the mushrooms, without burning. Salt & pepper to taste.
When mushrooms are done, add the RAW pasta! Toast pasta, stirring continually, til slightly browned and beginning to soften.
Add the broth, a bit at a time, stirring, as the liquid is absorbed.
Add beans and a little more broth, or water, as if it were risotto. Continue adding stock til pasta is "al dente" and liquid absorbed, about 12-15 minutes.
At this point add the cheese and continue to stir, adjusting salt & pepper.
Turn off heat and toss in frozen peas, stir and allow to sit a few minutes.