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In a large bowl, beat together flour, salt, butter, peanut butter, sugars, milk, and vanilla until smooth and combined.
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Using a small cookie scoop, portion cookie dough onto the bottom of 10 pecan sandies cookies. {This is about the same as one heaping tablespoons of cookie dough.} Top the cookie dough with a second cookie, bottom side facing the dough. Gently press down until the cookie dough reaches the edge of the cookies. Repeat with remaining cookies.
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In a microwave safe bowl, heat white chocolate chips for 1 minute in the microwave. Stir. Heat for another minute. Stir. Continue to heat for 30 seconds at a time, stirring between each interval, until chocolate is melted and smooth.
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Dip one half of each cookie sandwich in the melted white chocolate. Place on a Sil-Pat or parchment paper lined baking sheet. Repeat with remaining cookie sandwiches. Reheat white chocolate as needed if it becomes stiff.
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Place cookie sandwiches in the fridge until white chocolate sets.