Preheat the oven to 425 degrees. Meanwhile, combine the tomatoes, garlic cloves, 4 tablespoons of oil, and 4 tablespoons Manischewitz in a resealable bag and gently toss to combine. Let sit at room temperature until oven is ready.
Line a small rimmed baking sheet with foil. Spread the tomatoes, cut side up, along with the garlic pieces in a single layer. Pour any juices from the bag over the tomatoes. Sprinkle with kosher salt and freshly ground black pepper.
Transfer to the oven and roast for 30 to 40 minutes, until tomatoes are somewhat shriveled but not dry and a few are just starting to brown. Remove and let sit in the pan about 10 minutes.
Place ¼ cup of olive oil in a small jar. Remove the paper and tough stem ends from the roasted garlic cloves and press cloves through a garlic press or thoroughly mash them into the jar of oil. Add ¼ teaspoon kosher salt. Secure the lid and shake to break up the garlic and thoroughly combine (it will still be chunky).
Gently toss the tomatoes with ½ teaspoon to 1 teaspoon Manischewitz. Taste, and add a few more drops of wine if needed to reduce the acidic bite of the tomatoes. Don’t overdo this—they should not taste like wine.
Heat the broiler or a grill on high and toast the bread slices. Remove. Brush a layer of garlic oil on each bread slice (making sure each slice has a few bits of garlic). Spoon on a couple of tablespoons of tomatoes in a mostly single layer. Sprinkle with basil or oregano and serve immediately.