Heat milk to 115°, add 1 TBSP sugar, stir to dissolve, sprinkle yeast over milk and whisk to blend. Allow yeast to foam up, about 5 minutes, then whisk in eggs. Combine remaining 4 TBSP sugar with flour and salt in bowl of stand mixer. Add milk mixture and mix with paddle attachment until just combined. Add butter one piece at a time, blending well with each addition. Mix on medium speed about a minute, the dough will be sticky but will release from the sides of the bowl. Gather into a tight ball and place in buttered med. bowl and cover with plastic wrap. Let dough rise in warm, draft-free spot until doubled, about 1 to 1-1/2 hours.
Preheat oven to 375°. Divide dough into 12 pieces, keeping the dough covered until needed. Roll each piece on lightly floured parchment, using your fingers and the parchment, into a long rope about 16 to 17 inches long. Gently twist into pretzel shape (I practiced with a piece of string) and set on baking sheets lined with greased parchment. Cover loosely with plastic wrap as you prepare the next pretzel. Brush with egg white and water completely and sprinkle with sea salt crystals or turbinado sugar.
Set oven racks to top third and bottom third of oven. Bake one in top and one in bottom of oven for 9 minutes and then switch for about 9 more minutes. They should be a nice golden color. Cool on wire racks.
Great warm: plain or serve with a spicy mustard.
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