Preheat oven to 425ºF/220ºC. Ensure bird's cavity is empty. Stuff cavity with garlic, ginger, and lime leaves. Place onion pieces on the bottom of the roasting pan. Place chicken on top of onions. Brush chicken with melted butter. Sprinkle with kosher salt and pepper. Pour white wine into base of pan. Place in oven for 15 minutes.
Reduce oven temperature to 350ºF/175ºC and place carrots, fennel, and baby potatoes. Lightly sprinkle veggies with salt. Cook the vegetables and chicken until the chicken breast meat registers at 165ºF/75ºC, about 20 minutes/lb. If the liquid evaporates off, add a bit more white wine.
10 minutes before the chicken is done, add the asparagus pieces.
Once done, removes chicken and veggies from the pan to a serving dish. Set the pan with the juices on the stovetop at medium-high heat (if minimal juices, top up slightly with more chicken broth). While waiting for the juices to start boiling, whisk together the flour and broth until smooth. Once the juices start to boil, slowly add the flour mixture, stirring continuously, until desired thickness for gravy is achieved. Remove from heat. Serve.