In a large bowl or stand mixer, combine warm water, yeast, and honey. Let stand 5 minutes until foamy. Add bread flour, 2 tablespoons olive oil, and kosher salt. Mix on low speed until a shaggy dough forms, then knead on medium-low for 8 minutes until smooth and elastic. The dough should clear the sides of the bowl but stick slightly to the bottom.

Transfer dough to an oiled bowl, turn to coat, and cover with plastic wrap. Let rise at room temperature until doubled, about 1 to 1.5 hours. Press the dough gently - it should leave a slight indentation that slowly springs back.

Pour 2 tablespoons olive oil into a 9x13 inch pan, tilting to coat the bottom and halfway up the sides. Turn dough out into the pan and use your fingertips to dimple and stretch it to fit. It will spring back - that is fine. Cover and let rest 20 minutes.

Return to the dough and use oiled fingertips to dimple and stretch it again, working it into the corners. The dimples should be deep - they will hold the olive oil. Cover and let rise until puffy and nearly doubled, about 45 minutes.

Preheat oven to 450°F. Press halved cherry tomatoes cut-side-up into the dough, nestling them into the dimples. Scatter chopped rosemary over top, drizzle with remaining 3 tablespoons olive oil, and sprinkle with flaky sea salt.

Bake 22-25 minutes until the top is deeply golden and the internal temperature reaches 200°F. The tomatoes should be blistered and jammy. Immediately run a spatula around the edges and transfer to a wire rack. Let cool at least 15 minutes before slicing - this sets the crumb and keeps it from getting gummy.