Preheat oven to 400 degrees F (200 degrees C).
Zest the Lemon (1) into a small bowl, then cut lemon into quarter-inch sliced rounds, and set aside.
Pressing down with the flat side of the knife, smash the Garlic (20 clove) and set aside.
Remove the stems from the Fresh Rosemary (0.25 ounce) and discard. Finely chop the rosemary, and set aside.
Pat dry Chicken (1) with paper towels and evenly rub half of the Butter (2 tablespoon) over the chicken. Season each piece with Salt (1/4 teaspoon) and Ground Black Pepper (1/4 teaspoon).
Lift up the skin of the chicken pieces and evenly spread the chopped garlic, and half of the rosemary underneath the skin of the chicken. Place the lemon slices under the skin.
Evenly rub the lemon zest and remaining rosemary over the chicken pieces.
Place the chicken on a sheet pan lined with parchment paper and place in the oven. Roast for 35 minutes until the chicken is cooked through and the skin is golden brown.
Meanwhile, in a medium saucepan over medium high heat, bring the Milk (10 fluid ounce), one and a half cups of water, and Salt (1/4 teaspoon) to a simmer.
Add the Polenta Grits (4 ounce) and reduce the heat to low and cover, stirring occasionally. Cook for 20 minutes, stirring occasionally.
When the grits are finished cooking, add the Cheddar Cheese (3 ounce) and the remaining Butter (2 tablespoon) and stir to combine. Remove from heat and hold for plating.
In the center of two plates, place the cheese grits. Top with the roasted garlic chicken.