In a large bowl, combine 1¾ cups (420 grams) room temperature water and 2 tablespoons (28 grams) oil; add flour, salt, granulated sugar, and yeast. Stir with a rubber spatula or wooden spoon until a cohesive dough forms. (Dough will be shaggy and tacky.) Cover and let rise in a warm, draft-free place (75°F/24°C) for 1½ hours, folding dough in bowl every 30 minutes. (To fold, use wet or oiled hands to reach under one side of dough; gently stretch up, and fold over center; repeat on all sides of dough. (See more below))
Line a 13x9-inch baking pan with parchment paper, letting excess extend over sides of pan. Brush remaining 2 tablespoons (28 grams) oil onto parchment.
Turn out dough into prepared pan; using just your fingertips, gently stretch dough to about a 10x8-inch rectangle. (If dough is tight and will not stretch completely, let stand for 5 to 10 minutes and then try again.)
In a small bowl, stir together brown sugar and cinnamon. Sprinkle half of sugar mixture (about ¼ cup or 43 grams) onto dough. Starting at one short side, carefully roll up dough into a log. Place dough lengthwise, seam side down, in pan. Let stand for 10 minutes. Using your fingertips, gently stretch dough to fill pan. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size and jiggly, 45 minutes to 1 hour.
Preheat oven to 425°F (220°C).
Dimple dough using your fingertips, touching pan through dough without tearing dough.
Add melted butter to remaining brown sugar mixture, whisking until combined. Spoon onto dough.
Bake until golden brown and an instant-read thermometer inserted in center registers 190°F (88°C), 15 to 20 minutes. Let cool in pan for 10 minutes. Using excess parchment as handles, remove from pan.
In another bowl, whisk together cream cheese and confectioners’ sugar; whisk in milk until smooth. Drizzle onto warm focaccia. Serve warm. Store in an airtight container for up to 3 days.