Adjust the racks in the oven to cook with two racks. Heat the oven to 425 degrees F.
Make four large foil squares. Place a head of garlic in each square. Top the heads of garlic with a generous splash or two of olive oil. Create a foil packet around each garlic head and seal well. Place the garlic onto a small sheet pan and place into the oven and cook for 1 hour.
While the garlic is roasting, slice the squash in half through the middle (equator). Scoop out the seeds. Place each squash half, flat side down and cut into 1 ½ to 2-inch slices.
Place the squash onto a large foil lined rimmed sheet pan. Evenly distribute 2 tablespoons of olive oil on the tops of the squash (if this does not cover all the squash, add a bit more to lightly top each squash slice). Evenly distribute the 1/2 teaspoon kosher salt and pepper (to taste) onto the squash. Place into the oven and roast for 25 to 30 minutes.
Turn off the oven and remove the garlic packets but keep the squash in the oven to keep warm.
Meanwhile, remove the garlic from the foil packs and cool for 5 to 10 minutes. Squeeze out the roasted garlic (think toothpaste tube!) into a small mixing bowl. Add the tarragon, 3 tablespoons of olive oil, sugar, red wine vinegar and 1/4 teaspoon salt (optional). Stir and smash the garlic to combine and set aside.
Remove the squash from the oven and serve warm with the roasted garlic tarragon spread. Salt to taste.