As with any other kitchen, what is considered essential in a vegetable-forward kitchen depends on what you like to cook. If you like stir-fries, then you might want to grab a wok. If you have a fondness for braising, as I do, then you might rely heavily on a shallow Le Creuset braising pan.
While I've listed some of my favorite, most essential tools, I didn't mention my food mill, which I use only for two purposes (tomato sauce and applesauce) yet wouldn't be without, or my salad spinner. Nor did I mention hands, which are the best tools for feeling the food you're cooking; or noses, for smelling; or ears, for hearing when a process subtly changes on the stove; or eyes for discerning the beauty or flaw contained in a vegetable. You don't have to buy these; you're equipped with your senses already.