Bring a large pot of salted water to a boil, then add the fregola. While the fregola is cooking, warm the short rib slices in the braising liquid over low heat.
Cook the fregola until al dente, about 8 minutes. Drain, place in a serving dish, toss with the grated cheese and butter, then place the warmed short ribs on top. Garnish as desired with Fresno slices and shaved Parmigiano-Reggi