For sponge: In the bowl of a stand mixer, whisk together ½ cup (120 grams) warm water and yeast by hand until dissolved and well combined. Add flour; using the paddle attachment, beat at low speed until combined, about 30 seconds, stopping to scrape sides of bowl. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size and very small bubbles appear on surface, about 30 minutes.

For dough: Add 2 cups (254 grams) flour, ½ cup (120 grams) warm water, oil, and salt to sponge; beat at low speed just until combined. Switch to the dough hook attachment. Beat at low speed until dough is smooth, just barely sticky, and elastic, 7 to 9 minutes; add up to remaining ¼ cup (32 grams) flour, 1 tablespoon (8 grams) at a time, if dough is too sticky. (Dough should pass windowpane test; see Notes.)

Oil a large bowl. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 20 to 30 minutes.

Lightly oil a rimmed baking sheet. (See Notes.)

Punch down dough; cover and let stand for 10 minutes. Turn out dough onto a clean surface, and divide in half. Place one half smoothest side down. (Keep remaining dough covered with plastic wrap.) Shape dough into a 6×5-inch rectangle, one long side closest to you. Fold top long side toward center, and press to seal. Bring bottom long side up to meet other long side in center; press to seal. Moving from left end to right end, use your right thumb to depress along center of dough while folding dough lengthwise in half; simultaneously use fingertips to seal seam. Roll seam side down; fold and pinch ends under to create a 9×2½-inch loaf with rounded edges. Place on prepared pan. Repeat with remaining dough, and place 2½ to 3 inches away from other loaf on pan. Cover and let rise in a warm, draft-free place (75°F/24°C) until puffed and dough holds an indentation when poked, 18 to 20 minutes.

Preheat oven to 400°F (200°C).

Gently brush loaves with egg white. Using a lame, a razor, or a very sharp paring knife, score bread with 4 (3½-to 4-inch-long) diagonal cuts.

Bake until golden brown and an instant-read thermometer inserted in center registers 205°F (96°C), 14 to 17 minutes, rotating pan halfway through baking. Remove from pan, and let cool completely on a wire rack. Leave oven on.

For topping: In a small microwave-safe bowl, stir together oil and garlic; heat on high until warm and fragrant, about 1 minute. Stir in basil and Italian seasoning.

Using a serrated knife, cut loaves in half lengthwise. Brush garlic oil onto cut sides, evenly dividing garlic slices among loaves. Place bread, cut side up, on a parchment paper-lined baking sheet; sprinkle evenly with cheeses.

Bake until cheese is melted, 6 to 10 minutes. Garnish with basil and Italian seasoning, if desired. Serve immediately.