How to Make It
In a large pot of boiling salted water, cook the tagliolini until al dente.
Meanwhile, in a large, deep skillet, heat the olive oil. Add the shallot and cook over moderately high heat until softened, about 1 minute. Add the eggplant pieces in an even layer and cook undisturbed until browned on the bottom, about 1 minute. Cook, stirring a few times, until tender, about 2 minutes longer. Add the vegetable stock and simmer for 1 minute. Add the tomatoes and mint, season with salt and pepper and cook over low heat for 4 minutes.
Drain the tagliolini, reserving 1 cup of the cooking water. Add the pasta to the skillet along with the butter and 1/4 cup of the Romano cheese and toss well. Add enough of the reserved pasta cooking water to moisten the pasta, then season with salt and pepper. Transfer the pasta to bowls and serve with extra Romano cheese.