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Step 1
Melt butter in a small skillet over medium heat until foamy, about 6 minutes. Continue to cook, stirring occasionally, until butter begins to sputter, about 2 minutes more. Add sage leaves and cook, stirring constantly, until sputtering subsides, milk solids are light golden brown, and sage leaves are crisp, 5–7 minutes. Using a slotted spoon, transfer sage leaves to a plate and lightly season with salt; set aside. Continue to cook butter, stirring constantly, until milk solids are deep golden brown, about 1 minute more. Pour brown butter into a heatproof measuring glass, scraping in milk solids. Let sit undisturbed until milk solids fall to bottom of glass, about 2 minutes. Carefully pour all but ¼ cup brown butter into a small bowl, leaving milk solids behind. Chill brown butter with milk solids until thickened and creamy but still soft; set aside for layering in the parathas.
Step 2
Whisk sugar, 3 cups (375 g) flour, and 1 Tbsp. Diamond Crystal or 1¾ tsp. Morton kosher salt in a large bowl. Add 1 cup warm water and 3 Tbsp. melted brown butter and mix with a wooden spoon until no dry spots of flour remain and dough comes together in a shaggy mass. Cover with a plate and let sit at room temperature 15 minutes.
Step 3
Knead dough in bowl until it forms a smooth mass, about 2 minutes. Transfer to an unfloured surface and continue to knead until smooth and elastic, about 8 minutes. (The dough will feel very sticky at first but will grow smooth and soft as you go. Try to avoid adding more flour if possible.)
Step 4
Roll dough against surface to form into a ball; return to bowl. Drizzle with 1 Tbsp. melted brown butter and turn to coat. Arrange seam side down and cover with plastic wrap. Let sit at room temperature at least 1 hour and up to 4 hours (if you poke the dough with your finger it shouldn’t spring back).
Step 5
Using a bench scraper or chef’s knife, divide dough into 8 pieces. Working with 1 piece at a time, cup dough in your palm and roll against work surface to form into a ball. Coat each ball with brown butter; cover with a damp towel, plastic wrap, or overturned bowl and let sit 20 minutes.
Step 6
Stir reserved chilled brown butter to evenly distribute milk solids into fat and make sure it’s creamy and spreadable. Roll out 1 piece of dough on a lightly floured surface until as thin as possible. Don’t worry about size or shape at this point; you just want it to be superthin. Using your fingers or an offset spatula, spread a heaping teaspoonful of chilled brown butter across dough (it doesn’t have to be even, just get it on there), dust lightly with flour, and break 3 sage leaves into pieces and scatter on top.
Step 7
Starting from the top, roll dough into a long snake. Fold ends inward until they meet at the center, then stack the 2 coils onto each other and press together firmly. Lightly dust with flour and place on a parchment-lined baking sheet. Repeat with remaining pieces of dough. Once all pieces have been coiled, cover and let rest at room temperature at least 2 hours or chill overnight.
Step 8
Heat a dry medium cast-iron skillet (10" or larger) over medium. Working one at a time, roll out dough coils on a lightly floured surface to 7"–8" rounds about ⅛" thick, rotating after each roll to keep evenly round. Brush off any excess flour with a pastry brush. Parcook paratha in skillet until just set but without taking on any color, about 2 minutes per side. Transfer to a clean baking sheet as you work.
Step 9
Brush pan with brown butter and place a parcooked paratha in middle of pan. Brush paratha with more brown butter and cook, turning every 30 seconds and adding more brown butter as needed, until golden brown and crisp, about 3 minutes. Wrap in a kitchen towel to keep warm and quickly scrunch to release any steam (this will keep them from getting soggy). Repeat with remaining parathas, stacking in towel as you go.
Step 10
Do ahead: Parathas can be parcooked 1 day ahead. Wrap tightly and chill, or freeze up to 3 months.