Fill a medium pot with 1-inch water. Bring to a simmer over medium heat, then reduce the heat to low. Using a medium size heat proof bowl (one that will nestle in the pot without touching the water), whisk together the yolks and sugar until smooth. Pour in the lime juice and zest and continue whisking until smooth. Nestle the bowl into the pot and whisk until thickened, about 7 minutes, or until the mixture has lightened in color and coats the back of a spoon. Immediately remove the bowl from the heat and start stirring in the butter one piece at a time. Wait to add the next piece until the previous one has been completely incorporated. Scrape into a clean bowl and cover with a piece of plastic wrap directly on the surface of the curd. Refrigerate at least 2 hours before using.
Place the phyllo tart shells onto a serving tray and just before serving, fill each tart shell 3/4 full with the lime curd. Refrigerate any leftover curd, it will last several weeks. Place the berries on top, garnish with a mint leaf and sprinkle with a light dusting of powdered sugar.