For dough: In a medium saucepan, heat milk, ½ cup (120 grams) water, and butter over medium-low heat, stirring occasionally, until butter is melted and an instant-read thermometer registers 120°F (49°C) to 130°F (54°C).
Place warm milk mixture and egg in Ankarsrum Assistent Original Mixer bowl with roller and dough knife attached. With roller resting on rim of bowl, mix on medium speed (3 o’clock) until combined. In a medium bowl, whisk together flour, sugar, kosher salt, and yeast. Reduce mixer speed to lowest setting (12 o’ clock), and gradually add flour mixture. Increase mixer speed to medium-low (2 to 3 o’clock), and mix just until a dough forms. Adjust arm to about 1 inch from side of bowl; set speed to medium-low (2 to 3 o’clock), and set timer for 10 to 12 minutes. Dough will be soft, smooth, and elastic when ready.
Turn out dough onto a clean surface; knead 3 to 4 times, and shape into a smooth round.
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, about 1 hour.
Lightly punch down dough. Cover and let stand for 10 minutes. Line 2 large baking sheets with parchment paper.
Turn out dough onto a very lightly floured surface, and roll into a 16x12-inch rectangle. Cut dough into 12 (4-inch) squares; place squares about 2 inches apart on prepared pans. Cover and let rise in a warm, draft-free place (75°F/24°C) until puffed, 30 to 45 minutes.
Meanwhile, for topping: Place tomato slices on several layers of paper towels; lightly sprinkle kosher salt on both sides of tomatoes. Let stand for 45 minutes. Gently brush off excess salt and blot dry with paper towels.
Preheat oven to 375°F (190°C).
Using a ½-cup dry-measuring cup dipped in flour, firmly press a 3-inch-wide indentation in center of each dough piece. Prick indentations with a fork 4 to 5 times. Brush dough pieces with 2 tablespoons (28 grams) oil.
Divide each burrata ball in half. Crumble or tear 1 portion of cheese into each indentation.
In another medium bowl, stir together tomato slices, garlic, red pepper, and remaining 2 tablespoons (28 grams) oil; spoon mixture onto cheese on each dough piece.
Bake until lightly browned, 12 to 15 minutes, rotating pans halfway through baking. Garnish with basil and sea salt, if desired. Serve warm.