Soak the Bulgur: Add the uncooked bulgur to a large mixing bowl. Pour in the 1% milk, stir so the bulgur is evenly moistened, then cover tightly with plastic wrap and refrigerate overnight, or about 8 to 12 hours, until softened.
Make the Dressing: In a small bowl, whisk together the olive oil, lemon juice, Dijon mustard, salt, and black pepper for about 30 seconds, until smooth and blended.
Build the Base: Place the chopped kale in a large serving bowl. Pour the dressing over the kale so it starts to coat the leaves.
Add the Main Ingredients: Add the shredded chicken and chopped Asian pear to the bowl. Cut most of the Manchego into small pieces, reserving a little to shave over the top later, then add the cut cheese to the bowl.
Add the Bulgur: Add all of the soaked bulgur to the bowl. It should be softened and ready to mix after chilling overnight.
Toss the Bowl: Toss everything together with tongs or a large spoon for 1 to 2 minutes, until the kale, bulgur, chicken, pear, and cheese are evenly combined and coated in the dressing.
Finish and Serve: Divide the mixture among serving bowls. Shave the reserved Manchego over the top and serve right away.