In a mortar or a small bowl, combine 4 1/2 tablespoons red curry paste, the 3 deseeded and chopped green chilies, and 2 tablespoons thinly sliced fresh lemongrass; mix until well combined and set aside.
Heat 1 1/2 tablespoons neutral oil in a heavy-bottomed pan over medium heat.
Add the curry paste mixture to the pan and cook, stirring, for about 1 minute until fragrant.
Add the 12 ounces chicken thighs (cut into strips) to the pan and stir to coat with the paste. Cook, stirring occasionally, until the chicken is lightly browned on the outside, about 3–4 minutes.
Pour in 3 cups low-sodium chicken broth, then add 1 1/2 tablespoons fish sauce and 1 1/2 teaspoons sugar; stir to combine.
Bring the mixture to a gentle simmer, reduce heat if necessary, and simmer uncovered for 15 minutes, until the chicken is tender and cooked through.
Add 8 baby corn (cut into bite-size pieces), 1 cup green beans (trimmed and cut into 2-inch pieces), and 1 small eggplant (cut into bite-size pieces). Stir to submerge the vegetables in the broth.
Simmer uncovered for an additional 5 minutes, until the vegetables are tender but still slightly crisp.
Remove the pan from the heat and stir in 1/2 cup fresh basil leaves and the juice of 1 lime until the basil wilts.
Taste and adjust seasoning if needed, then serve.