Heat oven to 375°F and arrange a rack in the middle. Season chicken pieces generously with salt and pepper.

Heat oil over medium heat in a large, oven-safe braiser until shimmering then add half the chicken pieces. Let cook, undisturbed, until browned and easily pull away from the bottom of the pan, about 5 minutes. Turn and repeat on the other side, transfer to a clean plate. Brown the remaining chicken on both sides, then transfer to the plate.

Return the pan to the heat and add the shallots, ginger, and cardamom. Season with salt and pepper and cook, stirring constantly, until starting to brown, about 1 minute. Add wine and scrap up any browned bits that are stuck to the bottom of the pan with the back of a wooden spoon. Add chicken broth, honey, and orange juice and bring to a boil.

Place chicken in the pan skin side up, cover and transfer to the oven. Let cook until chicken is no longer pink in the middle, about 30 minutes. Remove from oven and scatter rhubarb around the chicken. Cover and return to oven for another 15 minutes or until rhubarb is tender when pierced with a knife. Taste and add more salt and pepper as needed and serve.