In a large mixing bowl, combine sourdough discard, warm water, 2 tablespoons olive oil, honey, and yeast. Stir until well combined and let sit for 5 minutes until bubbly.
Gradually add flour and 1 teaspoon salt to the wet ingredients, mixing with a wooden spoon until a shaggy dough forms. Turn dough out onto a floured surface and knead for 5-7 minutes until smooth and elastic.
Place dough in a lightly oiled bowl, cover with plastic wrap, and let rise in a warm place for 1-2 hours until doubled in size.
Preheat oven to 425°F. Pour 2 tablespoons olive oil into a 9x13 inch baking pan, spreading to coat the bottom. Gently transfer the risen dough to the pan, stretching it to fit. Use your fingertips to create dimples across the surface.
Drizzle with additional olive oil, sprinkle with flaky sea salt and rosemary leaves. Let rest for 20 minutes while oven preheats.
Bake for 20-25 minutes until golden brown and crisp on top. The focaccia should sound hollow when tapped on the bottom.
Remove from oven and let cool in the pan for 10 minutes before transferring to a wire rack. Serve warm or at room temperature.