In a food processor, pulse 12 oz. mushrooms until finely ground. (Depending on your food processor, you might be left with some pieces that are a little bigger than others, and that's okay.) Thinly slice remaining 4 oz. mushrooms.
In a large skillet over medium-high heat, heat 1 Tbsp. oil and 1 Tbsp. butter until butter melts. Cook sliced mushrooms, stirring frequently, until browned and nearly crispy, about 8 minutes; season with salt. Transfer mushrooms to a plate.
In same skillet over medium-high heat, heat remaining 1 Tbsp. oil and 1 Tbsp. butter until butter melts. Cook pureed mushrooms, stirring occasionally, until beginning to brown and most of the moisture is evaporated, about 10 minutes.
Reduce heat to medium and add shallot and garlic; season with salt. Cook, stirring, until shallots are softened, about 5 minutes. Add broth, scraping bottom of pan, and bring to a simmer. Add acini di pepe; season with salt. Reduce heat to medium-low and continue to cook, stirring occasionally so pasta doesn’t stick to bottom of pan and adding more broth if liquid is evaporating too quickly, until pasta is al dente, about 12 minutes.
Stir in cream and cheese and cook, stirring frequently, until cheese is melted, 2 to 3 minutes more. Stir in caramelized mushrooms before serving.
