Gently toss apricots with 3 tablespoons sugar. Place remaining 5 tablespoons sugar on a rimmed plate and dip both sides of each brioche slice in sugar, coating well. Meanwhile, melt 2 tablespoons butter in a large saute pan over medium heat until foaming. Add 2 brioche slices to pan and cook until golden brown on bottoms, 2 to 3 minutes. Flip slices, add 1 tablespoon butter, and cook until other sides are golden brown. Transfer to a plate and repeat with remaining 2 slices.
Wipe out pan and increase heat to medium-high. Add remaining 4 tablespoons butter and cook, swirling pan occasionally, until butter is golden brown and fragrant, about 3 minutes. Add apricots and salt and cook, swirling pan to coat apricots in butter, until heated through, about 1 minute more.
Remove pan from heat, add water, and swirl to create a smooth sauce. Divide brioche among 4 plates. Top each with apricots, sauce, and a scoop of ice cream. Serve immediately.