Roasted Plums With Tahini Dressing

Preheat the oven to 400°F. Line a baking sheet with parchment paper. Arrange the fruit, cut side up, on the prepared baking sheet. Drizzle with the olive oil and season well with the salt and pepper to taste.
Sprinkle the fruit with all but a pinch of the fresh herbs. Place the baking sheet in the oven and immediately reduce the heat to 250°F. Roast until the fruit is very soft and juicy and starting to caramelize, about 2 hours. (Alternatively, turn off the oven after 1 hour and leave the fruit in the oven overnight. This will produce a more leathery result. Either way is good!)
In a medium bowl, combine 3 tablespoons of the lemon juice, the tahini, 3/4 cup water, salt, and the ice cube. Whisk vigorously until the mixture comes together. It should lighten in color and thicken enough that it holds an edge when the whisk is dragged through it.
Remove the ice cube if any remains unmelted and adjust the seasoning, adding more lemon juice and salt until the sauce is addictive—you will know. Scrape the sauce into a shallow serving dish and hide it from the eaters in your house until ready to serve.
Layer a plate with the roasted fruit, then drizzle with the tahini dressing. Sprinkle with the reserved fresh thyme or oregano and a pinch of flaky sea salt.