Heat a grill to medium-high.

Brush both sides of pineapple slices with oil.

Grill pineapple slices, turning occasionally, until lightly charred at edges and fruit is cooked through, about 8 minutes.

Transfer pineapple to a cutting board and let cool to room temperature.

Roughly chop grilled pineapple.

Divide pineapple, sugar, limes, and mint equally among four large glasses.

Muddle until mint is mashed and fruit releases its juices.

Add rum and muddle to incorporate.

Fill glasses with ice.

Divide seltzer between glasses.

Stir gently to mix.

Garnish with mint sprigs.