Adjust oven rack to lower-middle position and heat oven to 425 degrees.
For the filling: Peel peaches, then halve and pit each. Using small spoon, scoop out and discard dark flesh from pit area. Cut each half into 4 wedges. Gently toss peaches and sugar together in large bowl; let stand for 30 minutes, tossing several times. Drain peaches in colander set over large bowl.
Whisk 1/4 cup of drained juice (discard extra), cornstarch, lemon juice, and salt together in small bowl. Toss peach juice mixture with peach slices and transfer to 8-inch-square glass baking dish. Bake until peaches begin to bubble around edges, about 10 minutes.
For the topping: While peaches are baking, in food processor, pulse flour, 3 tablespoons sugar, baking powder, baking soda, and salt to combine. Scatter butter over and pulse until mixture resembles coarse meal, about ten 1-second pulses. Transfer to medium bowl; add yogurt and toss with rubber spatula until cohesive dough is formed. (Don't overmix dough or biscuits will be tough.) Break dough into 6 evenly sized but roughly shaped mounds and set aside.
To assemble and bake: After peaches have baked 10 minutes, remove peaches from oven and place dough mounds on top, spacing them at least 1/2 inch apart (they should not touch). Sprinkle each mound with portion of remaining 1 teaspoon sugar. Bake until topping is golden brown and fruit is bubbling, 16 to 18 minutes. Cool cobbler on wire rack until warm, about 20 minutes; serve.