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- Preheat oven to 325°F. Line a large rimmed baking sheet with parchment paper.
- Microwave 1 1/2 tablespoons butter in a small microwavable bowl on high until melted, about 30 seconds.
- Stir together oats, nuts, flour, brown sugar, cinnamon, and salt in a medium bowl. Drizzle in oil and melted butter; stir until well coated.
- Place mixture on prepared baking sheet, and shape into an even, compact 5-inch disk. Bake until deeply browned and fragrant, about 25 minutes (crumble will not be set). Let cool on baking sheet about 25 minutes (do not turn off oven). Crumble into pieces. Put aside.
- While crumble cools, heat remaining 1 tablespoon butter in a large ovenproof skillet over medium-high until foamy. Arrange pear halves, cut sides down, in skillet. Cook, undisturbed, until brown around edges, 4 to 5 minutes.
- Transfer skillet to oven. Bake until pears are tender, 10 to 20 minutes (depending on ripeness of pears). Remove from oven; transfer pears face up to a large plate.
- Return skillet to heat over medium. Add balsamic vinegar and cook, stirring constantly, until just slightly thickened, about 2 minutes. Remove from heat. Note: it will continue to thicken as it cools.
- Spread 1 or 2 tablespoon of yogurt onto each of 6 plates; top with pear halves and fill the fruit centers with crumble pieces. Drizzle about 1 1/2 teaspoons of the balsamic sauce over each serving.