Preparation

To make the garlic confit, place the garlic cloves in a small saucepan with enough oil to cover by 1 inch. Heat over medium heat until small bubbles rise in the oil. Reduce the heat to its lowest possible setting and gently simmer the garlic, stirring occasionally, for 40 minutes, or until the cloves are very tender and pale golden. Remove from the heat and let the garlic cloves cool in the oil. Store in an airtight container in the refrigerator for up to 1 week.

To make the tostada toppings, remove any leaves from around the stems of the eggplants, taking care to leave the stems attached. Pierce the eggplants several times with the tines of a fork. Place the eggplants in a plastic freezer bag, leaving it unsealed, and place the bag in the microwave. Microwave on high until the eggplants begin to soften, about 5 minutes.

Meanwhile, in a medium bowl, whisk together the soy sauce, vinegar, and sesame oil. Add the mushrooms and set aside to marinate while you grill the eggplants, flipping them periodically.

Using tongs, remove the eggplants from the bag and lay them directly over a medium-high flame on the stovetop. Cook until the bottom begins to fully char, about 3 minutes. Gently turn the eggplants with tongs and repeat the 3-minute char on the other side. (Alternatively, use a commercial or culinary blowtorch to char the eggplants for 3 minutes per side.) Set the eggplants aside to cool for 15 minutes.

Working with one eggplant at a time, use tongs to hold the eggplant by its stem as you gently peel the skin away from the flesh using a knife (a butter knife will work) or spoon. Try to get as much of the burnt skin off as you can, but if you miss a little bit, it will just enhance the smoky flavor of the resulting puree. Transfer the eggplant flesh to a food processor. Add 4 garlic confit cloves, season with salt, and pulse to thoroughly combine. The goal is not a silky puree but a slightly rustic, textured product.

Heat the olive oil in a sauté pan over medium heat. Remove the mushrooms from the marinade, add them to the pan, and cook until they just begin to soften and release their liquid but keep their texture, about 5 minutes.

To cook the tostadas, preheat the oven to 250°F.

Arrange the tortillas on a baking sheet. When the oven comes to temperature, place the pan in the oven for 10 to 12 minutes, until the tortillas are dry. This will make them fry better. Pour enough oil into a sauté pan to come ¼ inch up the sides. Heat over medium-high heat until the oil is sizzling but not smoking. Using tongs, add a single tortilla at a time to the hot oil. Bubbles should form on the surface of the tortilla immediately as you put it in the oil. If they do not, the oil is not hot enough. Fry the tortilla until golden brown, stiff, and crisp, 30 seconds to 1 minute per side. Remove the fried tortilla using the tongs, letting excess oil drain back into the pan as you do so. Transfer the tortilla to a paper towel–lined plate to absorb excess oil and immediately sprinkle with salt. Repeat to fry the remaining tortillas.

To build the tostadas, top each tortilla with about ¼ cup of the eggplant topping. Arrange about ¼ cup of the mushrooms on top of the eggplant. Scatter the cilantro and mint leaves over the mushrooms and garnish with the pickled onions.