Preheat oven to 375 degrees F. Center 2 racks in the oven.
Line 2 baking sheets with silpat nonstick baking mats or parchment paper.
In bowl of an electric mixer fitted with the paddle attachment, cream butter and both sugars until light and fluffy, about 4 minutes. Add salt and vanilla, and mix to combine. Add egg, and continue beating until well combined.
In a medium bowl, whisk together flour and baking soda. Slowly add dry ingredients to butter mixture. Mix on low speed until just combined. Stir in chopped pecans and both chocolates.
Using a 1-ounce ice-cream scoop or a tablespoon, scoop out dough, and place about 6 balls on each baking sheet, about 3 inches apart. Flatten each ball slightly, and gently press a pecan half in the center.
Bake 7 minutes, rotate pans between oven shelves, and bake until just brown around the edges, 6 to 8 minutes more. Remove from oven, and let cool slightly before removing cookies from baking sheets to cool on wire racks. Repeat process with remaining dough.
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