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Cafe Prima Pasta
[Full disclosure: I was invited to a dinner here on the house. As always, my reviews remain unbiased.]
Italian restaurants are vegetarian-friendly by default: noodles and tomato sauce, what could be easier? However, finding something delicious to eat beyond eggplant parmigiana is less common. Cafe Prima Pasta is trying to change that with their "Veg Out Tuesdays" six-course vegetarian tasting menu, as well as a regular menu of vegetarian options (though I believe you need to specifically ask for it when you go).
The tasting menu was great, a full review of it can be found here. My personal favorites of the night were the Grillata (an insanely perfect plate of grilled vegetables), the zucchini rolls with sun-dried tomato and arugula, and the fiocci alla pera (pasta "packages" filled with cheese and pear). Some items on the main menu are vegan-able, and they were very accommodating to requests.
It's a cozy, dimly-lit spot perfect for a date, the service was impeccable, and they have a renowned early bird special. I seriously can't wait to go back just for the Grillata... Recommended!