Bring 6 cups of water to a boil over high heat. Add cardamom, star anise, and salt. Boil rice, uncovered, for 25 minutes, until al dente. Drain and discard cardamom pod and star anise. Put rice in a large bowl.
Charred Scallion Vinaigrette
Smash and peel garlic. Peel and roughly chop ginger.
Cut apart scallion tops (dark green) from scallion bottoms (white and light green). Put green scallion tops over a hot grill or gas flame on the stove top for 15-20 seconds. Watch them carefully, they will burn like paper! Remove from heat. Set aside white and light green part of scallion.
Combine charred scallion tops, rice vinegar, oils, honey, salt, garlic, and ginger in a blender. Blend until smooth.
Assemble the Salad
Shred or cut carrots into julienne. Roughly chop cilantro. Slice white and light green part of scallions.
Pour scallion vinaigrette over still warm cooked brown rice in bowl. Add carrot, cilantro, and white part of scallions. Toss to combine. Adjust flavor for salt, vinegar, and honey, adding more if needed. Garnish with sesame seeds and eggs.
*The rice is soaked for shorter cooking time. If the rice isn’t soaked, cooking time will be 35-40 minutes.