In a mini food processor, finely chop the lemongrass.
In a large skillet, heat the vegetable oil. Add the lemongrass and shallots and stir-fry over high heat until the shallots are golden brown, about 2 minutes. Add the cauliflower, asparagus, carrots and red bell pepper along with 1/2 cup of the water; cover and cook over moderately high heat, stirring a few times, until the vegetables are crisp-tender, about 3 minutes. Stir in the coconut milk, soy sauce and the remaining 1/4 cup of water and bring to a simmer. Remove from the heat and season with pepper. Stir in the basil and bean sprouts. Transfer the stir-fried vegetables to bowls and serve with rice.