The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
2. Explicitly ORDER BY After GROUP BY (modified query below): By default, the database sorts all 'GROUP BY col1, col2, ...' queries as if you specified 'ORDER BY col1, col2, ...' in the query as well. If a query includes a GROUP BY clause but you want to avoid the overhead of sorting the result, you can suppress sorting by specifying 'ORDER BY NULL'.

Optimal indexes for this query:

ALTER TABLE `Ingredients` ADD INDEX `ingredients_idx_ingredientid` (`IngredientID`);
ALTER TABLE `Recipe_Ingredients` ADD INDEX `recipe_ingredients_idx_recipeid` (`RecipeID`);

The optimized query:

SELECT
        DISTINCT Recipes.RecipeTitle 
    FROM
        Recipes 
    INNER JOIN
        Recipe_Ingredients 
            ON Recipes.RecipeID = Recipe_Ingredients.RecipeID 
    INNER JOIN
        Ingredients 
            ON Recipe_Ingredients.IngredientID = Ingredients.IngredientID 
    GROUP BY
        Recipe_Ingredients.Amount,
        Recipes.RecipeTitle 
    HAVING
        Recipe_Ingredients.Amount = max(Recipe_Ingredients.Amount) 
        AND Recipes.RecipeTitle IN (
            SELECT
                Recipes.RecipeTitle 
            FROM
                Recipes 
            INNER JOIN
                Recipe_Ingredients 
                    ON Recipes.RecipeID = Recipe_Ingredients.RecipeID 
            INNER JOIN
                Ingredients 
                    ON Recipe_Ingredients.IngredientID = Ingredients.IngredientID 
            GROUP BY
                Recipes.RecipeTitle,
                Ingredients.IngredientName 
            HAVING
                Ingredients.IngredientName IN (
                    'garlic'
                )
        ) 
    ORDER BY
        NULL