Fill a large pot with water and 1 Tablespoon salt and bring to a boil. Add pasta and cook 10-12 minutes, or until al dente. Reserve 1 cup of pasta water and drain.
Drizzle a large skillet with olive oil and add chopped bacon, heat over medium low; cook 8-10 minutes, stirring occasionally, until the bacon is crisp. Remove bacon from pan with a slotted spoon, leaving fat in pan.
Increase heat to medium and add garlic. Cook until fragrant, about 30 seconds.
Add tomatoes, a pinch of salt, and 1/2 tsp black pepper. Cook 5-7 minutes, until tomatoes have burst and softened, scraping skillet occasionally. Stir in half of the cooked bacon.
Increase heat to medium-high, add pasta and toss to coat in sauce. Add ½ cup of the reserved cooking water and the arugula; stir until wilted.
Add remaining pasta water to skillet as necessary to thin sauce. Toss with remaining bacon and cheese and season with salt + pepper, to taste.