Heat oil in a large Dutch oven over medium-high. Add chicken; cook, turning occasionally, until browned on all sides, 10 to 12 minutes. Transfer chicken to a plate. (Do not wipe Dutch oven clean.) Reduce heat to medium. Add onion, garlic, and ginger; cook, stirring often, until mixture is fragrant and onion softens, 2 to 3 minutes. Stir in rice, salt, and pepper. Add stock, and bring to a boil over medium-high; immediately reduce to a simmer over medium-low, and cook, uncovered and stirring occasionally, until rice is just tender, 8 to 10 minutes.

Return chicken to Dutch oven. Cook, uncovered, stirring occasionally, until rice mixture is creamy, chicken is tender, and an instant-read thermometer inserted into thickest portion of chicken registers 165°F, 7 to 10 minutes.

Remove chicken from Dutch oven, and transfer to a cutting board. Shred chicken into bite-size pieces using 2 forks; remove and discard bones. Stir shredded chicken back into rice. If porridge becomes too thick, add additional stock, 1/2 cup at a time, as needed to reach desired consistency. Stir in fish sauce, and garnish with fried shallots and sliced scallions. Serve with lemon wedges.