Quarter the tomatoes, then cut away the core (try not to sacrifice seeds). Layer tomato pieces in a shallow dish, overlapping a bit; season each layer with kosher salt and pepper as you go. Smash 3 garlic cloves and add them to the dish, along with the oregano; season generously with pepper.
Slowly pour olive oil over so that it barely kisses the top of the tomatoes (you might not need all of it, or you might need a little more, depending on the dimensions of your dish). Let tomatoes marinate at room temperature for up to 2 hours, or cover and refrigerate for up to 1 day. (If oil has solidified after being chilled, let mixture sit at room temperature until it is liquid again, about 30 minutes.)
To serve, toast the bread and rub the slices with the remaining 1 garlic clove while still warm. Use a slotted spatula or spoon to transfer the tomatoes onto the toasts. Season with a few dashes of vinegar and top with flaky salt, pepper, and basil.
Strain and refrigerate the marinating liquid in a tightly sealed container for up to 2 weeks and use in vinaigrettes, to season beans and cooked grains, or to make another batch of tomatoes.