Heat the oven to 350°F with a rack in the middle position. In a 10-inch oven-safe skillet over medium, melt the 2 tablespoons butter, then add 107 grams (½ cup) sugar and the honey; stir with a silicone spatula until the sugar is evenly moistened. Off heat, arrange the apples cut side down facing the same direction in a tightly packed ring around the pan. Arrange as many wedges as will fit in the center, then tuck the remainder into any gaps. Sprinkle with ¼ teaspoon salt.

Set the pan over medium-high and bring to a vigorous simmer. Reduce to medium, cover and cook, without stirring, until the apples begin to soften and have released a generous amount of liquid, 5 to 8 minutes. Uncover and cook, without stirring, until a very dark, coppery caramel develops around the fruit at the edge of the pan, 15 to 20 minutes. Occasionally rotate the pan for even cooking, but do not stir. Set aside off heat.

In a small bowl, whisk the flour, baking powder, cardamom and remaining ½ teaspoon salt. In a medium bowl, whisk the remaining 143 grams (⅔ cup) sugar and eggs. Whisk in the buttermilk and vanilla, then whisk in the melted butter. Gently whisk in the flour mixture just until incorporated; it is fine if there are a few small lumps. Scrape the batter onto the apples; spread into an even layer. Bake until the cake is well risen and golden brown, about 35 minutes.

Remove the skillet from the oven and set on a wire rack; cool for 10 minutes. Run a silicone spatula around the sides of the cake to loosen. Invert a 12-inch heatproof platter onto the skillet and, using potholders, hold the platter and skillet together while carefully inverting them; lift off the skillet. If needed, reposition any fruit that was dislodged. Cool completely.