Bring a large pot of heavily salted water to boil; add pasta and cook, stirring occasionally, until about 2 minutes less than the package directions (it will finish cooking in the sauce). Drain, reserving 1 cup of the pasta water.
Meanwhile, met 1 tablespoon of butter and 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the mushrooms, season with salt and cook until they release their juices and begin to caramelize, about 10-15 minutes, stirring occasionally. Set aside.
Melt 2 tablespoons of butter and 1 tablespoon of olive oil in large skillet over medium heat. Add the Porcini Paradiso; cook, swirling the pan, until very fragrant, about 1 minute. Add a pinch of salt and stir; take 1 tablespoon of this porcini Paradiso mixture out and set aside.
Add ½ cup of the reserved pasta water to the porcini Paradiso skillet; bring to a simmer. Add pasta and remaining tablespoon of butter to the skillet; toss with tongs until pasta is evenly coated and perfectly al dente. (Add more pasta water if sauce seems dry.)
Remove pan from heat and add pecorino; stirring and tossing with tongs until cheese melts.
Transfer pasta to serving dish or bowl, top with sauteed mushrooms and pieces of burrata cheese then drizzle with remaining porcini Paradiso mixture.