In a large bowl, whisk the active starter, warm water, and honey until milky. Add the bread flour and 2 tablespoons of olive oil and mix by hand until no dry flour remains. Cover and rest for 30 minutes.
Sprinkle the salt over the dough with 1 teaspoon of water. Pinch and fold the dough in the bowl until the salt is fully absorbed and the dough comes back together.
Over the next 90 minutes, do 3 sets of stretch and folds, about 30 minutes apart: with a wet hand, stretch one side of the dough up and fold it over the middle, turning the bowl a quarter turn each time until you have gone all the way around.
Cover and let the dough rise at about 75°F (24°C) until it has grown by about 50 percent and looks domed and bubbly, 4 to 6 hours from mixing. For the overnight option, refrigerate the covered dough at this point for 12 to 48 hours.
Line 2 baking sheets with parchment. Lightly oil the counter, turn out the dough, and cut it into 16 equal pieces of about 60 g each.
Roll each piece into a loose 4-inch log. Cover with a towel and rest for 15 minutes so the gluten relaxes.
Roll each log under your palms into a 10-inch (25 cm) rope. Twist the ends in opposite directions 2 or 3 times if you like, then place on the baking sheets about 1 inch apart, 8 per sheet.
Cover loosely and proof for 45 to 60 minutes (60 to 90 minutes if the dough was refrigerated) until slightly puffy. Meanwhile, heat the oven to 425°F (220°C) with racks in the upper and lower thirds.
Brush the breadsticks generously with olive oil, then sprinkle with the chopped rosemary and a pinch of flaky salt each.
Bake for 16 to 20 minutes, swapping and rotating the trays halfway, until deep golden brown on top and underneath. Start checking at 14 minutes, since the honey speeds browning.
Brush lightly with a little more olive oil as they come out of the oven. Cool on the tray for 5 minutes and serve warm.
