Preheat oven to 350 degrees. Slice away the root and stem end from the sweet onions, then cut into 1/4-inch thick slices. Trim away the roots from the bunch onions and slice, using all of the bulb and a portion of the green. Heat the butter and oil in a baking pan that is just large enough to hold the sliced onions in a layer about 1 inch deep. Add the onions and toss gently to thoroughly coat each piece. Sprinkle with the salt, sugar, bay leaves, and thyme, and toss again.
Bake in the oven, turning them often, until they are soft and a deep golden brown, about 45 minutes to 1 hour. Remove from the oven and let cool to room temperature.
Discard the bay leaves. Stir in the vinegar a little at a time, until the right level of "zip" is achieved. Pack the onions into dry, clean jars with lids. Store in the refrigerator. The onions will keep for up to 3 weeks. Spread on burger buns for a special treat.
Grilled and Roasted Sweet Onions with Pine Nut Butter
1/2 cup plus 2 tablespoons pine nuts (divided), toasted
4 medium sweet onions
1 tablespoon olive oil
3 ounces unsalted butter, softened
1/2 teaspoon lemon zest
1/2 teaspoon chopped fresh rosemary
1/4 teaspoon freshly ground black pepper
1/4 teaspoon salt, or to taste
1/3 cup freshly grated Parmesan cheese
Lemon wedges and rosemary sprigs for garnish
Toast the pine nuts in a 350 degree oven for 6 to 7 minutes, or until golden brown. Cool. Caution: pine nuts burn easily.
Preheat the oven to 375 degrees and fire up an outdoor grill. Peel the onions and cut them in half, top to bottom. Brush onions with oil and place cut side down on the preheated grill. Barbecue until grill marks form. Place on a cookie sheet and finish cooking in the oven until tender, about 25 minutes.
Meanwhile, make the pine nut butter. Place the 1/2 cup pine nuts in the bowl of a food processor and pulse several times until finely ground. Add butter, lemon zest, rosemary, black pepper and salt. Process until mixture is well blended. Spread the tender onions liberally with pine nut butter. Return to the oven and cook just until butter is melted, about 2 minutes.
Serve onions warm, sprinkled with grated Parmesan cheese and additional toasted pine nuts. Garnish plates with lemon wedges and rosemary sprigs.