Frittata: In a nonstick 10-inch skillet, heat the oil over medium heat. Add the pancetta and cook, stirring frequently, until golden brown and crispy, about 6 to 8 minutes.
While the pancetta is cooking, in a medium bowl, whisk together the eggs, whipping cream, salt and pepper. Pour the egg mixture over the cooked pancetta and stir once to incorporate. Cook the egg mixture, without stirring, until the eggs are almost set and the bottom is golden brown, about 5 to 6 minutes. Slide the frittata onto a dinner plate and invert back into the skillet until cooked through, about 3 to 4 minutes longer. Transfer the frittata to a cutting board and cut into 4 wedges.
Mayonnaise: In a small bowl, combine the mayonnaise and chives until smooth.
To assemble the sandwiches: Divide the mayonnaise mixture and spread it evenly over 1 side of each bread slice. Arrange the arugula, a slice of cheese and 2 tomato slices on 4 of the bread slices. Lay the frittata wedges on top of the tomatoes. Cover with the remaining bread slices and serve.