In a medium mixing bowl and using your hands, combine flour, water, and yeast until no dry flour remains. The dough should feel sticky and soft—if it seems stiff, drizzle in 1–2 tablespoons more water. Cover and let sit for 30 minutes.

Massage in salt and olive oil until incorporated. Cover and let sit for an additional 30 minutes.

Using damp hands, scoop and lift a handful of dough, stretch it until you feel resistance, then fold it toward the center of the dough. Turn the bowl, then repeat until all the dough edges are stretched to the center. Be cautious not to rip the dough. Cover and let rise for 30 minutes. Repeat this process two more times, allowing the dough to rise for 30 minutes each time. After the final fold, the dough should look smoother and more elastic.

Preheat oven to 425°F after the third round of dough folds. Line a baking sheet with parchment paper. Then, while the dough is resting and/or rising, prep the squash (or other) topping.

In a large bowl, use your hands to combine all ingredients except the shallot. Spread out evenly on the baking sheet, making sure the squash pieces do not overlap. Bake for 10 minutes. Remove from oven, toss with shallots, and set aside.

Grease a muffin pan generously with olive oil. Increase the oven temperature to 450°F.

Split dough evenly into 12 balls. Place each ball into muffin pan, cover (another muffin tray or baking pan inverted works well), and let rise until doubled in size, about 45–60 minutes; times vary, depending on room temperature.

Brush dough and fingers with olive oil. Dimple dough repeatedly with your fingers. Add topping to each muffin cup, and be sure to press it down as firmly as possible into the dough. Bake for about 18–20 minutes, reducing oven temperature to 425°F halfway through.

Brush warm rolls with olive oil immediately after baking to keep them moist Serve warm or at room temperature.