Strain the porcini, reserving the soaking liquid. Squeeze them dry, chop them into small pieces, and set aside. Strain the soaking liquid though a fine sieve or a paper coffee filter; set aside. Bring a large pot of salted water to a boil for cooking the pasta. Meanwhile, in a large skillet over medium-high heat, heat the oil and 2 tablespoons of the butter. Add the fresh mushrooms and cook briskly, stirring frequently, until lightly browned and most of their liquid has evaporated, about 5 minutes. Add the shallot, garlic, rosemary, and the drained, chopped porcini. Cook, stirring briskly, until the shallot is soft, about 4 minutes. Add the chicken pieces, season with salt and pepper, and cook for another 2 minutes. Pour in the wine and the reserved porcini soaking liquid; bring to a boil. Simmer uncovered until the chicken is tender and cooked through, about 12 minutes. Meanwhile, cook the pasta until just tender. Drain the pasta, leaving drops of water clinging to it, and add it to the skillet. Add the vinegar and capers; heat gently for a few minutes to let the pasta drink up the juices. Stir in the remaining 1 tablespoon butter and taste for salt and pepper. Serve warm with the grated Romano, if you like.