Scatter the thyme leaves among the compartments of 2 large ice cube trays. Fill the trays with ginger beer and freeze at least 6 hours and preferably overnight.
Preheat the oven to 400 degrees F.
Put the pineapple slices on a nonstick baking sheet. Brush both sides very lightly with vegetable oil and sprinkle them evenly with the sugar; sprinkle very lightly with salt as well. Roast in the oven for 20 minutes. Remove from the oven and flip the slices.
Put in the oven and continue roasting until they are golden, about 10 minutes more. Remove from oven and cool slightly in the pan.
Transfer the ginger beer ice cubes to a food processor and pulse until broken down and fluffy. Transfer to a small cake pan or baking dish.
To serve, put 2 slices of warm pineapple on each dessert plate; top with a scoop of ginger ice and garnish with a small sprig of thyme.
If not using the ginger ice immediately, refreeze. To loosen it, scrape with a heavy fork until fluffy. Ginger beer is very spicy and the spiciness is enhanced when frozen. For milder ice, use natural ginger ale or ginger soda.