On the stovetop, combine sugars, vinegar, turmeric, and salt in a large nonreactive pot. Simmer syrup ingredients on medium-high heat for about 5 minutes, until combined. Stir regularly, so the syrup doesn’t bubble up.
Add sliced jalapeños and garlic to the syrup mixture and bring to a boil, then reduce to a simmer. Stir occasionally and continue cooking for 5 minutes; remove from heat.
Put coriander seeds into a pint-sized jar. Using a slotted spoon or tongs, transfer cooked jalapeños to the jar, leaving the syrup behind in the pot. Lightly pack the jar and leave 1/2 inch of head space.
Return syrup to a boil and simmer until reduced by about third, 8–10 minutes. Ladle the syrup into the jars, covering jalapeños and leaving 1/2 inch of head space. Once jars cool, place them in the refrigerator for up to 3 months.
Don’t throw away any extra syrup! Save it to use in marinades, dressings, and cocktails (see recipe on page 80), or mix with fruit for a sweet and spicy kick. And if you don’t have leftover syrup from the making, you can do the same with what’s left in the jar once the jalapeños are gone.