Cut the lemongrass into 3-inch segments, then cut each one in half lengthwise and slice it into thin matchsticks.
Use the flat side of a knife to crush the garlic slightly, leaving the cloves whole, and do the same to the ginger slice.
Place the lemongrass matchsticks, garlic cloves, and ginger slices into an extra-large teabag or square of cheesecloth and tie the top with string, making a bouquet garni.
Place the bag in a medium saucepan, and add the broth, water, soy sauce, and sugar. Cover pan, bring to a boil over high heat, then turn heat to low and simmer for 10 minutes.
Remove the bag of herbs, re-cover the pan, and turn heat as low as possible to keep warm.
Remove the tips from the asparagus, and place them in a small bowl. Slice the asparagus stalks into 1/2-inch pieces, and place them in a separate bowl.
In a large saucepan (about 4 quart), heat 1 tablespoon of the oil over medium, then add the asparagus tips and sauté until al dente and slightly crispy, 3 to 4 minutes.
Remove the tips from the pan and place them back in their small bowl. Add another tablespoon of oil to the pan, then the asparagus pieces and sauté until al dente, 5 to 6 minutes.
Add the sliced basil and mint leaves, stir and cook for 30 seconds, then remove from heat and place the mixture back in the bowl, still separate from the tips.
Add the remaining 3 tablespoons of oil to the saucepan, then add the sliced shallots. Sauté until the shallots are softened and beginning to brown, 8 to 10 minutes.
Add the chile, garlic, and rice, and cook for about 8 minutes, stirring constantly, until the rice starts to have a toasted aroma.
Add the sherry and stir until the liquid is gone. Now we can start adding the broth: using a ladle or heatproof measuring cup, add 1/2 cup of hot broth to the rice, stirring constantly.
Stir until the liquid is absorbed, then add another 1/2 cup of broth. Repeat in this way, stirring the whole time, until all the broth is gone and the rice is creamy and tender with a slightly firm center, which will take about 30 minutes.
Add the asparagus-basil mixture (not the tips!) and cook, stirring constantly, until the asparagus is tender, 5 to 10 minutes.
Remove from heat, stir in the lime juice, and let the risotto rest for 5 minutes.
Transfer risotto to bowls for serving, and top each one with the asparagus tips. Serve hot, with lime wedges at the table if desired.