How to Make It
Trim and discard the root and vine ends of the squash. Cut two ¼-inch-thick slices crosswise from the middle section (save any scraps for another use).
Heat a small nonstick skillet (but large enough to fry 2 eggs) over medium heat. Add the bacon and cook until crisp, 6 to 7 minutes, turning once. Transfer the bacon to a paper towel to drain; set aside the skillet with the rendered bacon fat.
Meanwhile, cut the bagel in half. Spread 2 tablespoons of the cheese onto the cut side of each half and set aside.
Preheat a grill pan over medium-high heat. Sprinkle the squash slices on both sides with the salt and pepper and drizzle with the 1 teaspoon oil, dividing it equally. Add the squash slices to the pan and cook, turning once, until grill marks form and the squash is tender; 5 to 8 minutes.
While the squash cooks, heat the skillet that you cooked the bacon in over medium-low heat. If there is not enough fat in the skillet to fry the eggs, add a bit of oil. Crack the eggs into the skillet and cook to the desired doneness.
To assemble each sandwich, place a squash slice on top of a cheese-spread bagel half. Top it with a tomato slice and then an egg. Crumble up the bacon and scatter half on top of each sandwich, along with half the scallions. Yum!