Heat the oil in a heavy large nonstick frying pan over medium heat. Add onion and saute until tender, about 5 minutes. Add the garlic and saute for just a minute. Add the squash, eggplant, rosemary and thyme and saute for 8 to 10 minutes. Add the wine and broth and bring to a simmer over medium-high heat. Decrease the heat to medium-low and simmer until the squash is tender and the liquid is reduced by about half, stirring occasionally, about 10 minutes. Add the shrimp and simmer gently until almost cooked through, stirring occasionally, about 5 minutes. Season, to taste, with salt and pepper.
Meanwhile, bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender but still firm to the bite, stirring often, about 5 minutes. Drain pasta. (Alternatively, you can use dried pasta, which will take 8 to 10 minutes to cook.)
Toss the pasta, squash mixture, and butter in a large bowl until the liquid thickens slightly and coats the pasta. Transfer the pasta mixture to a wide shallow bowl and serve.