Adjust an oven rack to the lowest position and place a pizza stone or inverted baking sheet on it. Preheat the oven to 500°F for at least 30 minutes to ensure the stone is hot enough to crisp the dough.

Heat the olive oil in a large skillet over medium-high heat until it shimmers. Add the onions and salt and cook until they begin to soften.

Reduce the heat to medium-low and cook, stirring occasionally, until the onions are deep golden brown and jammy, about 40 to 45 minutes. If the onions begin to stick or brown too quickly, add a tablespoon of water to deglaze the pan and keep them moving.

Divide the dough into two equal pieces. On a lightly floured surface, stretch or roll each piece into a 12-by-6-inch rectangle or oval—aim for an even thickness so it bakes uniformly.

Spread the caramelized onions evenly over the dough, leaving a half-inch border around the edges. Top with the blue cheese, walnuts, and thyme.

Slide the flatbreads onto the preheated stone or baking sheet. Bake until the crust is deeply browned and the cheese is bubbling, about 8 to 12 minutes.

Transfer to a cutting board and let rest for a few minutes to allow the cheese to set. Serve warm while the crust is still crisp.