Heat oven to 350°F. Place chicken on rimmed baking sheet and season with 1/2 tsp. each salt and pepper; let sit 5 min. Meanwhile, finely grate zest of half of lemon into small bowl, then squeeze in 1 tbsp. juice. Mix in oil, ginger, and cumin seeds. Place lemon halves in chicken cavity, then rub entire chicken with oil mixture. Tie legs together and roast 40 min. Increase oven temp to 425°F. Scatter carrots and shallots around chicken and roast until vegetables are golden brown and tender and temperature of chicken thighs registers 165°F on instant-read thermometer, 25 to 30 min. Transfer chicken to cutting board and let rest 10 min. before carving. Toss vegetables with any juices on sheet, then sprinkle with feta and serve with chicken.