Heat oven to 425°F. Slice butter into pats and place on a small sheet pan. Slice through the whole head of garlic on its equator, revealing a cross-section of each clove. Place both halves cut-side down on top of the butter. Cover tightly with aluminum foil. Roast garlic and butter 35-45 minutes, until garlic is very soft.
Meanwhile, put spinach in a blender or food processor and put up water to boil for pasta. When the garlic and butter are ready, pick up the garlic with tongs and use a knife to release any sticky cloves into the sheet pan (most should fall in on their own). Pour the garlic and butter into the blender.
Blend the butter/garlic and spinach until mostly smooth, scraping down the blender as needed.
Cook the pasta according to package directions, reserving a half cup of pasta water before draining. Add 1/4c of pasta water to the blender and blend for at least a minute, until very smooth. Add zest from the lemon and a little juice, adjusting to taste.
Return pasta to pot with sauce over low heat. Heat through while stirring for a minute, until sauce coats pasta. Serve with parmesan cheese.