Heat olive oil in a large skillet over medium-high heat; cook and stir bacon until softened, but not browned, about 3 minutes. Add cauliflower and continue to cook until cauliflower is lightly browned, stirring frequently, 5 to 7 minutes.
Stir tomatoes and garlic into cauliflower mixture, cooking for 2 to 3 minutes. Add chicken stock, balsamic vinegar, sugar, and anchovy paste and mix.
Cover skillet and reduce heat to low; simmer until cauliflower is tender, about 5 minutes more. Remove lid and increase heat to medium-high. Continue cooking until liquid is reduced, about 5 minutes. Season with salt and pepper. Sprinkle with parsley to serve.