Add the 1 (15-oz) can full-fat coconut milk, 2 to 4 Tbsp green curry paste (start with 2 Tbsp and add more to taste), 1/2 cup fresh basil, the peeled 12-inch nub fresh ginger (roughly chopped), and 1/2 tsp sea salt to a blender; blend until smooth and well combined.
Pour the blended sauce into a large skillet with a lid and heat over medium-high until it comes to a gentle boil (small bubbles across the surface).
While the sauce is heating, peel and chop the 3 large carrots and cut the red bell pepper into matchsticks. Add the carrots and bell pepper to the skillet and stir to combine.
Chop the 1 lb chicken thighs into bite-sized pieces. Add the chopped chicken, 1 cup chicken broth, and 1 cup white rice to the skillet; stir to distribute the rice and chicken evenly.
Increase heat briefly to bring the skillet to a full boil, then reduce heat to maintain a gentle simmer. Cover and cook for 15 minutes without lifting the lid.
Meanwhile, cut the 1 medium zucchini into bite-sized pieces, chop the small crown of broccoli into florets, and chop 1 to 3 leaves of chard if using.
After 15 minutes, remove the lid and stir in the zucchini, broccoli, and chard (if using). Cover and cook another 5 to 8 minutes, until the rice is tender and the vegetables reach your desired doneness.
Remove from heat, taste and adjust seasoning if desired, and serve in bowls garnished with additional fresh basil and lime wedges.