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1
Fill kitchen sink with about 2 inches of cold water. Melt butter in a 2- to 3-quart heavy saucepan over moderate heat and cook, stirring occasionally, until butter turns golden with a nutlike fragrance and flecks on bottom of pan turn a rich caramel brown, 10 to 12 minutes. (Butter will initially foam, then dissipate. A thicker foam will appear and cover the surface just before butter begins to brown; stir more frequently toward end of cooking.) Place pan in sink to stop cooking, then cool, stirring frequently, until butter starts to look opaque, about 4 minutes. Remove pan from sink and stir in sugar and vanilla.
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2
Whisk together flour, baking soda, and salt in a small bowl and stir into butter mixture until a dough forms. Shape into a ball, wrap with plastic wrap, and let stand at cool room temperature 1 to 2 hours (to allow flavors to develop).
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3
Put oven rack in middle position and preheat oven to 325u00b0F.
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4
Press a piece of dough into bowl of teaspoon, flattening top, then slide out and place, flat side down, on an ungreased baking sheet. (Dough will feel crumbly, but will become cohesive when pressed.) Continue forming cookies and arranging on sheet. Bake cookies until just pale golden, 8 to 15 minutes. Cool cookies on sheet on a rack 5 minutes, then transfer cookies to rack and cool completely, about 30 minutes.
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5
While cookies cool, heat preserves in a small saucepan over low heat until just runny, then pour through a sieve into a small bowl, pressing hard on solids, and cool completely.
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6
Spread the flat side of a cookie with a thin layer of preserves. Sandwich with flat side of another cookie. Continue with remaining cookies and preserves, then let stand until set, about 45 minutes. Transfer cookies to an airtight container and wait 2 days before eating.
