And this one too . . .

I found the website for Saveur magazine. Typing in "apples" brought up so many wonderful things!
From http://ourchocolateshavings.blogspot.com/2009/09/apple-pudding.html:

Apple Pudding
Serves 4

2 big apples (I used Cortland), peeled, cored and roughly chopped
1/2 lemon, juice and zest
2 x 1/4 cup of brown sugar
1/4 teaspoon of ground cinnamon
1/4 cup of self-rising flour
1 teaspoon of vanilla extract
50 grams of room temperature butter
1 egg

Preheat your oven to 350F.
In a small bowl, combine the apple pieces, lemon juice and zest, cinnamon and brown sugar. Set aside.

In a another bowl, using an electrical mixer, beat the butter and sugar (about 2 minutes). Add the the egg and vanilla extract until just combined. Slowly add in the flour until just combined. Divide the apple mixture into 4 individual ramekins and spoon over the flour mixture. Bake for 40-45 minutes. Enjoy!

Remind me to make this

Buttery Apple Cake-Tart

This recipe started life as Ligita's Quick Apple Cake, which is a classic recipe in itself. As things tend to do in my kitchen, however, this evolved, and now it's a close relative of Ligita's cake, but definitely its own dessert. For one, I bake it in a shallow tart pan, which allows for maximum crustiness and a somewhat lighter texture. I've also taken out the cinnamon, which I felt was masking the delicate flavor of the browned butter, and replaced it with a vanilla bean, since vanilla bean sauteed in brown butter is one of the best things ever, trust me. The result is something really unique, like I said, a cross between a cake and a tart, crisp and soft, buttery, fragrant and fruity. And trust me again, you will want some whipped cream or ice cream alongside.
Source: adapted from Classic Home Desserts by Richard Sax
Yield: one thin, 11-inch cake; serves 8

3 large tart apples, such as Granny Smith, peeled, cored and thinly sliced
1 teaspoon fresh lemon juice
3/4 cup (150g) plus 3 tablespoons sugar
3/4 cup (1 1/2 sticks/180g) unsalted butter
1/2 vanilla bean, split in half lengthwise (i.e. cut a bean in half crosswise, then split the half lengthwise)
2 large eggs, lightly beaten
1 cup (140g) all-purpose flour, sifted
1/4 teaspoon salt
Vanilla-flavored whipped cream or ice cream, for serving

Preheat the oven to 350F/175C. Generously butter an 11-inch (28cm) nonreactive tart pan or other similarly-sized glass or ceramic baking dish. Toss the apples in a bowl with the lemon juice and 2 tablespoons of the sugar. Spread the apples evenly in the prepared pan.

Combine the butter and vanilla bean in a small saucepan (not nonstick - you need to be able to see the butter change color). Cook the butter over medium until the milk solids are light brown and the whole thing smells deeply nutty, about 7-10 minutes. Watch carefully to avoid burning.

Allow to cool for a few minutes, then remove the vanilla bean (add it to your extract!) and pour the browned butter into a medium-sized bowl, scraping the black vanilla seeds and browned butter solids in too. Stir the 3/4 cup (150g) sugar into the butter. Gently stir in the eggs; stir in the flour and salt just until blended. Spoon the batter evenly over the apples and spread into an even layer. Sprinkle with the remaining 1 tablespoon sugar.

Bake until lightly golden and crusty, 30 to 40 minutes, or until a toothpick inserted in the center comes out clean. Cool in the pan on a wire rack. Cut into wedges and serve from the pan warm, with whipped cream or vanilla ice cream.

Update: so I made this and it was pretty good but just way too sweet. Next time I won't toss the apples with sugar and I'll cut the sugar in the custard to about 1/2 cup.