I highly recommend brineing either Cornish hens or chicken. It just makes them more tasty and juicy. So, combine the salt and sugar in a large deep pot; add cold water and stir until they dissolve. Once dissolved, add the hens and make sure they are submerged in the brine (you can use a plate to make them stay down if they insist on floating) brine for 1 hour, then rinse in cold water and dry well (oil and water don’t mix, so make sure they are dry).
While the hens are brinieng, prepare your vegetables.
If you prep the veggies in advance, you will want to put the parsnips and turnips (and potatoes if you cut them) into a bowl with ice water to keep them from turning ugly; drain and dry them well before proceeding to the next step)
Place all the vegetables in a large bowl, add 2 tablespoons olive oil and toss well. Add some thyme, salt, and pepper to your liking and toss again. Place the vegetables in the bottom of a roasting pan.
Heat oven to 375 F.
Inside of each hen, stick one of the rosemary sprigs, the sage, and ¼ lemon. Quickly truss the legs and wings to keep them close to the bird. Rub with 1 tablespoon olive oil, season with salt and pepper, and set on a roasting rack. Place this over the vegetables. (If you don’t have a roasting rack, place the hens directly on the vegetables.) Place in the oven shut the door, and go do something else for about an hour.
After your hour is up (did you do something fun? I hope so) the vegetable should be tender and the hens cooked, if not, let them go a little longer, you can kick up the heat to 400 °F if you want. Add the chicken stock and let cook in the oven for about 5 – 10 minutes more.
Remove the hens to a cutting board, tent loosely with foil, and allow to sit for 5 – 10 minutes.
Take the roasting pan to the stove and over medium-high heat, cook the vegetable, stirring occasionally, until the chicken stock and hen drippings have reduced and nicely glazed the vegetables and they are tender.
Remove the “stuffing” from the hens, cut into halves, and serve with the vegetables.