Make the marinade: in a medium saucepan combine 1/2 cup white vinegar, 2 tsp salt, 1 tsp sugar, chopped garlic, bay leaves, 1/2 tsp freshly ground black pepper, chopped red pepper, and 1 1/2 Tbsp dill. Simmer for 5 minutes.
Add 2 cups water to the saucepan, bring the mixture to a boil, then reduce heat and simmer for 5 more minutes.
Remove the saucepan from heat, stir in 1/2 cup vegetable oil, and set the marinade aside to cool slightly.
Prepare blanching water: in a large pot bring 16 cups water and 3 Tbsp vinegar to a boil to prevent mushroom browning.
Rinse the mushrooms, then trim and cut them into quarters or halves as needed (leave small mushrooms whole).
Place the prepared mushrooms into the boiling blanching water, stir, cover, and cook for 3 minutes.
Drain the mushrooms in a colander, then immediately transfer them to the warm marinade in a heatproof container.
Bring the mushrooms and marinade briefly to a boil for 2–3 minutes, then remove from heat and let cool to room temperature.
Cover and refrigerate the marinated mushrooms overnight before serving.