Preheat oven to 450˚F with rack in middle. Oil a baking sheet.

Halve apples lengthwise and remove core with melon-ball cutter or paring knife. Melt butter in a 10-inch heavy ovenproof skillet over medium heat and sprinkle with 1/2 tablespoon sugar. Arrange apple halves, cut side down, on sugar and cook, undisturbed, until sugar begins to caramelize, about 3 - 5 minutes. Transfer skillet to oven and bake apples until tender, about 15 minutes.

While apples are baking, cook remaining sugar with 1/4 teaspoon salt in a dry 8-inch heavy skillet over medium-high heat, undisturbed, until sugar begins to melt, about 2 minutes. Continue to cook, stirring occasionally with a fork, until sugar is melted into a deep golden caramel, 1-2 minutes more. Remove from heat. Add toasted walnuts, stirring to coat, then pour onto a baking sheet and cool 10 minutes. Break nuts into small pieces if necessary.

Stir together yogurt and 2 teaspoons honey.

Serve apples cut side up topped with yogurt and walnuts. Drizle with additional honey if desired.

Note: To toast walnuts spread them on a baking sheet; bake in a 350˚F oven until golden and aromatic.