1. In a medium saucepan, combine the rice with the 2 1/2 cups of water and bring to a boil. Reduce the heat to low, cover and cook for 15 minutes. Remove the pan from the heat and let stand, covered, for 5 minutes. Uncover and fluff the rice. Spread the rice on a large baking sheet and let cool to room temperature.
2. Meanwhile, in a heatproof bowl, soak the morels in the boiling water until softened, about 20 minutes. Rub them to loosen any grit, then lift out the morels. Let the soaking liquid stand for 5 minutes so the grit falls to the bottom. Pour off 1/2 cup of the soaking liquid, leaving any grit behind, and reserve.
3. Cook the asparagus in a medium saucepan of boiling salted water until just tender, about 4 minutes. Drain and rinse under cold water. Cut the asparagus into 1/2-inch lengths.
4. In a wok or very large skillet, melt the butter over low heat. Add the shallots and cook, stirring, until softened but not browned, about 4 minutes. Add the morels, asparagus and ham and stir-fry for 2 minutes. Add the rice and cook over moderate heat, breaking it up with a spatula. Add the reserved 1/2 cup of morel soaking liquid and stir-fry until heated through, about 4 minutes. Season with salt and pepper and stir in the sesame oil. Serve at once.
Make Ahead: The recipe can be prepared through Step 3 up to 1 day ahead.
Wine Recommendation: A dry, aromatic, stylishly acidic Riesling will have enough fruit to stand up to the assertive flavors of the morels, ham and asparagus. Look for a German example, such as the 1997 Robert Weil Kabinett Rheingau Halbtrocken, or an Alsace bottling, such as the 1997Lucien Albrecht.