Line a rimmed baking sheet with a double layer of paper towels and set a fine-mesh strainer over a large heatproof bowl; set aside. Using a sharp knife, chop garlic into approximately ¼- to ⅛-inch pieces. Alternatively, transfer whole garlic cloves to the bowl of a food processor and pulse until garlic is chopped into approximately ¼- to ⅛-inch pieces, 10 to 12 pulses.

If cooking on stovetop: Combine chopped garlic and oil in a 2-quart saucepan or wok. Place over medium-high heat and cook, stirring frequently with a heat-resistant rubber spatula, until garlic begins to bubble steadily, 2 to 3 minutes. Continue cooking, stirring frequently and scraping down sides and bottom of saucepan to ensure even cooking and prevent garlic from sticking and scorching, until garlic turns pale golden brown, 5 to 7 minutes longer. Working quickly, pour contents of saucepan into prepared strainer set over bowl. (Garlic will continue cooking for a brief period after draining, so do not allow it to get too dark.) If cooking in microwave: Combine garlic and oil in a large microwave-safe bowl and stir to break up any clumps. Microwave on high power for 5 minutes. Stir with a heat-resistant rubber spatula, scraping down sides of the bowl. Continue to microwave in 2-minute increments, stirring between each round, until garlic begins to turn lightly golden, 4 to 8 minutes total. Microwave in 30-second increments, stirring between each round, until evenly pale golden brown, 30 seconds to 1 minute and 30 seconds longer. Working quickly, pour contents of bowl into strainer set over bowl. (Garlic will continue cooking for a brief period after draining, so do not allow it to get too dark.)

Immediately transfer garlic to prepared baking sheet, spread out into an even layer, and season with salt. Using a fine-mesh cocktail or tea strainer, lightly dust garlic with powdered sugar (if using). Allow garlic to drain, then carefully lift top layer of paper towels and roll garlic onto second layer, blotting gently with the first. Allow fried garlic and garlic oil to cool to room temperature, then transfer to separate airtight containers, lining bottom of container for fried garlic with a folded paper towel. Store fried garlic at room temperature and garlic oil in the refrigerator.