How to Make It
Place a pizza stone or baking sheet in oven; preheat oven to 450°F. Remove dough from refrigerator; set aside at room temperature.
Whisk together flour and 1/4 cup of the milk in a small bowl until smooth. Heat remaining 1 cup milk in a small skillet over medium-high until bubbles form and milk just simmers. Stir in flour mixture; simmer, stirring often, until thickened and reduced to 1 cup, about 2 minutes. Remove from heat; let cool 5 minutes. Stir in sour cream and 1/2 teaspoon each of the salt and pepper; set aside.
Melt butter in a large skillet over high until foamy. Add onion, mushroom caps, garlic, and thyme; cook, stirring often, until mushrooms soften and release their liquid, 5 to 6 minutes. Add beef; sprinkle with remaining 2 teaspoons salt and 1 1/2 teaspoons pepper. Cook, stirring occasionally, until beef is browned and liquid has evaporated, 5 to 6 minutes. Remove from heat; let cool 10 minutes.
Roll dough into a 14-inch circle on a lightly floured work surface. Sprinkle a pizza peel or rimless cookie sheet with cornmeal. Place dough on prepared peel. Prick liberally with a fork, and brush with 1 1/2 tablespoons of the oil. Slide dough off of peel and onto hot pizza stone in preheated oven. Bake 3 minutes; remove from oven. Spread sour cream mixture in a circle on dough, leaving a 1-inch border. Top evenly with beef mixture and cheese. Return to oven, and bake at 450°F until cheese is bubbly and melted, 9 to 11 minutes. Remove from oven.
Brush crust with remaining 1 1/2 tablespoons oil. Sprinkle pizza with chives and paprika. Cut into 12 wedges.