Dough
Topping
FOR THE DOUGH Pulse flour, sugar, and yeast in food
processor until combined, about 5 pulses. With processor
running, slowly add ice water and process until dough is
just combined and no dry flour remains, about 10 seconds.
Let dough rest for 10 minutes.
Add oil and salt to dough and process until dough forms
satiny, sticky ball that clears sides of bowl, 30 to 60 seconds. Transfer dough to lightly floured counter and knead by hand to form smooth, round ball, about 30 seconds. Place dough seam side down in lightly greased large bowl or container, cover tightly with plastic wrap, and refrigerate for at least 24 hours or up to 3 days.
FOR THE TOPPING Heat 3 tablespoons oil in 12-inch
nonstick skillet over medium heat until shimmering. Stir
in onions, red peppers, sugar, garlic, salt, pepper flakes,
and bay leaves. Cover and cook, stirring occasionally, until
onions are softened and have released their juice, about 10
minutes. Remove lid and continue to cook, stirring often,
until onions are golden brown, 10 to 15 minutes. Off heat,
discard bay leaves. Transfer onion mixture to bowl, stir in
vinegar, and let cool completely before using.
Press down on dough to deflate. Transfer dough to
clean counter, divide into quarters, and cover loosely with
greased plastic. Working with 1 piece of dough at a time
(keep remaining pieces covered), form into rough ball by
stretching dough around your thumbs and pinching edges
together so that top is smooth.
Place ball seam side down on counter and, using your
cupped hands, drag in small circles until dough feels taut
and round. Space dough balls 3 inches apart, cover loosely
with greased plastic, and let rest for 1 hour.
Adjust oven racks to upper-middle and lower-middle
positions and heat oven to 500 degrees. Coat 2 rimmed
baking sheets with 2 tablespoons oil each. Generously coat
1 dough ball with flour and place on well-floured counter.
Press and roll into 14 by 5-inch oval. Arrange oval on
prepared sheet, with long edge fitted snugly against 1 long
side of sheet, and reshape as needed. (If dough resists
stretching, let it relax for 10 to 20 minutes before trying
to stretch it again.) Repeat with remaining dough balls,
arranging 2 ovals on each sheet, spaced ½ inch apart. Using fork, poke surface of dough 10 to 15 times.
Brush dough ovals with remaining 1 tablespoon oil and bake until puffed, 6 to 8 minutes, switching and rotating
sheets halfway through baking.
Scatter onion mixture evenly over flatbreads, from edge
to edge, then sprinkle with pine nuts, if using. Bake until
topping is heated through and edges of flatbreads are deep
golden brown and crisp, about 15 minutes, switching and
rotating sheets halfway through baking. Let flatbreads cool
on sheets for 10 minutes, then transfer to cutting board
using metal spatula. Sprinkle with parsley, slice, and serve.