Use a mortar and pestle or rolling pin to gently crack open cardamom pods to release their flavor and aroma. Seeds should be visible but not popping out. Set aside.

Roll lemons firmly against counter to soften their rinds. Halve and juice lemons; pour juice into a sealable container and refrigerate. Cut rinds into 1-inch chunks. In a large nonreactive mixing bowl, mix lemon rinds well with sugar and cracked cardamom pods. Cover with plastic wrap or a lid, and let stand at room temperature, stirring once every 45 minutes or so, until sugar has completely dissolved, about 3 hours. (You can let the mixture stand up to 12 hours, if desired.)

While the lemons macerate, use a spice grinder or mortar and pestle to pulverize the cardamom seeds into a fine powder. You should get between 2 and 3 teaspoons of powder. Set aside in an airtight jar until needed (see notes).

Stir the lemon chunks once more, tasting and smelling the mixture to ensure it has a cardamom aroma and flavor.

Add water, 8 ounces (1 cup) of reserved lemon juice, and 1 teaspoon ground cardamom to the macerated lemons (see notes). Stir well, then strain through a nonreactive fine-mesh strainer or piece of cheesecloth into a glass or ceramic container, pressing to express liquid; discard solids.

Stir ½ teaspoon ground cardamom and salt into the liquid. At this point, the concentrated cardamom lemonade can be refrigerated in a tightly sealed glass or other nonreactive container for up to 1 week.

To serve, pour lemonade over ice and adjust to taste with additional water or lemon juice, depending on personal preference; bear in mind, though, that the lemonade will be diluted as the ice melts.