Heat oil in a medium Dutch oven or heavy-bottomed pot over medium heat. Add carrots and garlic paste; cook, stirring constantly, until the garlic is fragrant, about 1 minute.
Stir in broth and bring to a boil over medium-high heat. Reduce heat to medium to maintain a simmer and cook, uncovered, until the carrots are crisp-tender, 4 to 5 minutes.
Whisk together cornstarch and water in a small bowl. Drizzle into the simmering soup; cook, stirring, until slightly thickened, about 1 minute.
Stir in rice, breaking up any clumps. Whisk eggs and lemon juice together in a medium bowl until frothy. Slowly whisk 1 cup of the hot broth into the egg-lemon mixture. Whisking vigorously, gradually add another 1 cup broth.
Whisk the egg mixture back into the soup; stir in chicken and salt. Remove from heat and stir until warmed through, about 2 minutes.
Ladle the soup into 6 bowls. Top with dill and cracked pepper.
