Position oven rack to the upper-middle position; preheat oven to 400°.

Line a baking sheet with parchment paper.

Whisk the flours, sugar, baking soda, cream of tartar, and salt together in a large bowl.

Work the butter into the dry ingredients with a fork until the mixture resembles coarse crumbs.

Combine the buttermilk and egg with a fork.

Add the buttermilk-egg mixture, raisins, and caraway seeds to the flour mixture; stir with a fork just until the dough begins to come together.

Turn out onto a lightly floured work surface and knead just until the dough becomes cohesive and bumpy; about 30 seconds (do not knead until smooth).

Pat the dough into a 6-inch round about 2 inches thick, and lay on the prepared baking sheet.

Cut a large 1/2-inch deep X into the top of the loaf using a serrated knife; brush top with 1 tablespoon melted butter.

Bake until golden brown and a toothpick inserted into the center comes out with just a few crumbs attached, about 40-45 minutes, rotating the pan halfway through baking.