Preheat the oven to 350°F.

Make the za’atar tomatoes. Put the tomatoes, oil, vinegar, garlic, ½ teaspoon of salt, and a good grind of pepper into a medium baking dish, roughly 12 x 8 inches/30 x 20cm. Cover tightly with foil and bake for 40–45 minutes, stirring halfway through, or until the tomatoes have just burst but aren’t completely falling apart. Remove the foil, gently stir in the za’atar and sugar, and let cool completely. Once cool, stir in the herbs (gently, so as not to break up the tomatoes).

Turn the heat up to 475°F. Line a large baking sheet roughly 16 x 12 inches/40 x 30cm in size with parchment paper.

Put half the butter into a medium saucepan over medium-high heat. Once melted, add the flour and cook, whisking continuously, for 30 seconds or until it smells like popcorn. Slowly pour in 1½ cups/360ml of the milk, whisking continuously to avoid any lumps, then add the garlic, ½ teaspoon of salt, and plenty of pepper, turn the heat down to medium, and cook for 5 minutes, stirring often, until quite thick and no longer floury-tasting. Set aside and cover with a piece of parchment paper, to prevent a skin from forming.

Meanwhile, prepare the polenta by first putting the remaining 1⅔ cups/400ml of milk, the water, 1½ tablespoons of the butter, 1¼ teaspoons of salt, and a good grind of pepper into a medium sauté pan (or saucepan) over medium-high heat. Once it gently bubbles, turn the heat down to medium-low, slowly add the polenta, whisking continuously to incorporate, and cook for 2 minutes, to thicken. Add the pecorino and the remaining 1½ tablespoons of butter and stir with a spatula until incorporated. Quickly transfer to the prepared baking sheet and spread out in a large oblong shape about ½ inch/1cm thick and 15 inches/38cm in length. Spoon the béchamel over the top and spread it so it covers the surface, leaving a ½-inch/1½cm rim exposed around the edges. Top evenly with the feta and the oregano sprigs and bake for 22 minutes, or until golden and bubbling on top and starting to brown around the edges. Let cool for 5–10 minutes.

Spoon about half the za’atar tomatoes on top of the baked polenta, serving the rest in a bowl alongside. Use a pizza cutter to easily cut the polenta into slabs and serve warm.