Melt butter (4 tablespoons) in small bowl (I used my Pyrex measuring cup); add minced garlic (3 cloves), chopped rosemary (from 3 sprigs, about 2 tablespoons), the zest of the two lemons, and plenty of kosher salt and black pepper to taste. Set aside.
Prepare chicken by removing giblets from cavity and patting dry with paper towels.
Liberally season the cavity with salt and pepper. LIBERALLY.
Cut the zested lemons in half; reserve juice and save rinds.
The butter mixture will have hardened slightly by now. Using your hands, slather the mixture liberally over every part of the chicken and under the breast skin (being careful not to tear the skin).
Stuff the cavity of the chicken with the lemon rinds, onion scraps, remaining 2 garlic cloves, and rosemary sprig/stems. Place in dutch oven on top of sliced onions and potatoes, if using.
Tie the legs of the chicken together tightly using kitchen twine.
Pour reserved lemon juice over the chicken.
Roast chicken UNCOVERED for 15 minutes at 475, then reduce heat to 350 and cook STILL UNCOVERED for approximately 20 minutes PER POUND, or until internal temperature reaches 165 degrees (about 1.5 hours for a 4.5 lb. chicken). The chicken should be uncovered the entire time it cooks, unless it seems like it's burning (see notes).
Allow the chicken to rest for at least 10 minutes before carving.
Basting: If you want to, baste the chicken approximately halfway through cooking process. You don't have to.
Salt and pepper: You want to salt and pepper liberally- I’d say at least 1 tablespoon of kosher salt for a 4ish lb. bird (up to 2 tablespoons, if you have a larger chicken that’s more like 8 lbs.). Pepper you can do to your taste- it will give it a nice kick if you use a lot (around 2 teaspoons) but you can definitely get away with only 1/2 teaspoon.
If chicken is burning: you should cook the chicken uncovered in the dutch oven, but if it starts to burn on top and the internal temperature is not high enough yet, you can place the lid on ajar to avoid direct heat and prevent further burning. Or, you can tent it with foil on top.
Other vegetables: You can add carrots or other root veggies, that take a long time to cook, in the bottom of the pan in place of or in addition to the potatoes. Note: I actually prefer to roast my potatoes/veggies separately because they get more browned, but it's super convenient to cook them in the same pot!
Slow cooker instructions: Place sliced onions in bottom of large slow cooker. Prepare chicken as directed above. Cover and cook on low for 8-9 hours or high for 4-5, until the chicken is falling off the bone. (this method will not make crispy skin, but will still be delicious!
Make it paleo/dairy free/Whole30: Use olive oil or ghee instead of butter.
The provided nutrition information does not include any added sodium from seasoning to taste, any optional ingredients, and it does not take brands into account. Feel free to calculate it yourself using this calculator or by adding the recipe to Yummly.