2 whole unpeeled heads of garlic, the top 1/4” of bulbs cut off with a sharp knife (leave the root end intact)
½ c. olive oil, divided
1 ½-2 lbs. fresh mushrooms, one type or a variety, trimmed, rinsed, patted dry, and quartered
2 lbs. green beans, regular or haricot verts, stems snipped off where necessary, rinsed and patted dry
2-3 tsp. coarse kosher salt, plus more to taste
¼ tsp. freshly ground black pepper, plus more to taste
Handful of fresh thyme sprigs
1 c. inexpensive balsamic vinegar (any generic brand works perfectly well)
To make vegetables, preheat oven to 425 degrees. Line 3 large baking sheets with parchment paper, or lightly oil them; set aside.
Place each bulb of garlic, cut side up, onto a doubled 8-inch square of aluminum foil paper. Lightly drizzle the tops of the garlic with olive oil. Bring the sides of the paper up over the garlic bulbs and gather the paper at the tops to seal. Place garlic packets directly on oven rack in preheated oven and roast for about 35 minutes, or just until garlic is tender and slightly caramelized. Transfer hot garlic packets to a cooling rack. Let cool for at least 10 minutes before unwrapping.
Toss mushrooms in a bowl with 3-4 tbsp. olive oil and 1 tsp. coarse kosher salt and ground fresh pepper, to taste. Remove the thyme leaves from 3-4 sprigs of thyme and toss evenly into mushroom mixture. Turn mixture out onto one of the baking sheets, spreading them out as much as possible. Roast in oven for about 20 minutes, moving mushrooms around after 10 minutes. Remove pan from oven and cover lightly with a sheet of aluminum foil paper; reserve.
Toss green beans in a large bowl with ¼ c. olive oil and 1 ½-2 tsp. coarse kosher salt. Spread green beans out between remaining 2 prepared baking sheets, and roast in preheated oven for 22-25 minutes.
While vegetables are roasting, make glaze. Place balsamic vinegar into a small saucepan and bring to a boil over medium–high heat. Immediately reduce heat and let vinegar simmer for about 7-8 minutes, stirring 2-3 times during the process, until vinegar is reduced by about half and has become syrupy. Be careful: the vinegar can turn from perfect syrup to a burned mess in seconds! Know that the vinegar will continue to thicken as it cools.
Before serving, arrange green beans on a large serving platter. Scatter reserved mushrooms over beans, and squeeze roasted garlic cloves from their skins onto the vegetables. Taste for seasoning, adding more salt and pepper, as desired.
Drizzle balsamic glaze decoratively over vegetable mixture, add a few grinds of pepper, and scatter some more fresh thyme over everything before serving. (The vegetables and glaze for this dish may all be made a day in advance. Vegetables should be refrigerated, and glaze can stay at room temperature. Before serving, reheat vegetables in a 400-degree oven until hot. Drizzle with room temperature glaze, scatter thyme sprigs on top, and serve.)