Halve grape tomatoes. Cut bacon into 3/4" pieces. Add spaghetti to boiling water and cook 7 minutes. Drain in colander. Spaghetti will finish cooking in a later step.

While spaghetti cooks, line a plate with a paper towel and heat 1/2 tsp. olive oil in a medium oven-safe pan over medium heat. Add diced bacon and cook 6 minutes, stirring often, until slightly crispy. Remove to towel-lined plate. Carefully pour all but 1 tsp. of bacon fat into a heat-proof container to chill before discarding.

Working quickly so eggs don't scramble, toss cooked bacon (reserving a pinch for garnish), liquid egg, heavy cream, spaghetti, oregano, Parmesan cheese (reserving a pinch to top frittata), 1/2 tsp. salt, and a pinch of pepper together in a medium mixing bowl.

Swirl pan so that reserved bacon fat covers entire pan, add frittata mixture, and top with remaining Parmesan cheese. Place pan in oven and cook 25-30 minutes, or until mixture is set (doesn't jiggle when you tap the pan) and cheese is lightly browned. Using an oven mitt, remove from oven and top with remaining bacon.

While frittata bakes, wash mixing bowl used to toss frittata mixture. Whisk together vinegar, sugar, and 1 Tbsp. olive oil in mixing bowl and season with a pinch of salt and pepper.

Carefully slide frittata out of pan and slice, or serve slices directly from pan. Toss arugula and grape tomatoes with vinaigrette and serve alongside.