Prepare a grill or grill pan for medium-high heat cooking.

Meanwhile, combine sugar, thyme leaves and 1/4 cup water in a small saucepan.

Set over high heat and bring just to a boil, stirring to dissolve sugar.

Let cool to room temperature.

Grill nectarines, flipping halfway through, until charred in parts and soft and juicy, 8 to 10 minutes total.

Let cool, then transfer to a large bowl.

Using a wooden spoon, mash nectarines until very juicy and pulpy.

Add thyme syrup and about 1 cup of the wine and stir well, continuing to muddle solids until completely mashed.

Strain mixture through a fine-mesh strainer into a large pitcher, pressing to extract as much liquid and nectarine pulp as possible; discard solids.

Pour remaining wine into the pitcher and stir to combine.

Fill 4 to 6 glasses with ice and pour in nectarine punch.

Garnish with thyme sprigs and nectarine slices.