Preheat the oven to 375 degrees F.
For the streusel topping: Put the flour and salt in a medium bowl and, using your hands, rub in the brown sugar. Stir in the melted butter with a fork until the mixture is evenly moistened. Pop into the freezer while you cut the fruit.
For the nectarines: Scatter the cold butter on the bottom of an 8-inch square shallow baking dish. Halve the fruit, pit and slice a thin piece off the round bottoms so they sit flat in the baking dish. Put the fruit cut-side up in the dish-it should fit snugly, but with a little space between the nectarines. Scoop up a heaping tablespoon of the streusel and press it into the center of each nectarine half. Scoop up another heaping tablespoon, squeeze it in your hand a bit and put it on top of each nectarine-no matter if some of it falls into the baking dish. Bake until the fruit is tender and the streusel crisp, 30 to 35 minutes.
For the topping: Whisk the brown sugar into the yogurt. Serve the nectarines warm or at room temperature with a dollop of cool sweetened yogurt.
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