Put a large pot of water on the stove to bring to a boil for pasta.
Preheat medium skillet over medium-high heat. Add chopped bacon and cook until crisp.
Salt water for pasta and add spaghetti to the pot. Cook to al dente, with a bite to it.
Remove bacon to paper towel lined plate with a slotted spoon and drain off most of the fat, return pan to heat and reduce heat to medium. Add extra-virgin olive oil, and 1 tablespoon butter. When butter melts into extra-virgin olive oil, add in garlic and the shallots, saute for 3 minutes.
To the garlic and shallots, add in flour and cook a minute more. Whisk in stock, bring to a bubble, about 30 seconds then stir in the cream. When cream comes to a bubble, add in blue cheese and a few grinds of black pepper. Stir until cheese melts. Reduce heat to lowest setting.
Drain pasta and toss with sauce to coat and combine evenly. Taste to adjust seasoning.
Scatter the arugula and bacon bits across the top of the pasta.