Bring first 4 ingredients to a simmer, without stirring, in a heavy nonaluminum Dutch oven (about 9 1/2 inches in diameter) over medium heat; cook, without stirring, 20 to 25 minutes or just until bubbles appear and temperature reaches 175° to 180°. (Do not boil.)
Stir gently, and return to a simmer. Cook, without stirring, 5 to 6 minutes or until temperature reaches 190°. (Do not boil or stir. Mixture will look curdled.) Remove from heat, and let stand 30 minutes.
Line a fine wire-mesh strainer with 3 layers of cheesecloth, and place over a bowl. Spoon mixture into strainer. Cover with cheesecloth; chill 12 to 24 hours. Remove cheese, discarding strained liquid.
Spoon cheese into a serving bowl; drizzle with olive oil, and sprinkle with salt and crushed red pepper. Serve with crackers. Refrigerate dip in an airtight container up to 2 days.