Heat the olive oil, when the oil is hot, add mushrooms, salt and sherry.
Cover, lower heat, cook until liquid is released from the mushrooms (about 10 minutes) and then drain and set aside.
Slice and toast bread slightly, just to dry it out a bit.
Whip up garlic mayonnaise (alioli) – Mix egg yolks with mashed garlic and salt. Let rest for 5 minutes. Stirring constantly, add olive oil VERY SLOWLY at first. After about half the oil has been incorporated and the mixture is thickening, thin it out with the vinegar. Continue adding olive oil, beating until a fairly thick emulsion is formed. Aïoli is thicker than traditional mayonnaise. Add a tablespoon of warm water at the end if a thinner emulsion is preferred. Add salt to taste.
Spread the alioli on the tostadas and top with mushrooms. Broil for about 30 seconds or until alioli starts to bubble.
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