Place rimmed baking sheet on rack and heat oven to 325 degrees. Line a 12-cup nonstick muffin tin with parchment paper muffin liners (do not use regular paper liners) or spray with vegetable oil spray. Bring a kettle of water to boil.
Meanwhile, add chopped bacon to a cold 12 inch skillet, then heat over medium-high heat. Cook bacon until crispy, 5 to 7 minutes. Transfer bacon to paper towel–lined plate.
Add 1½ cups cottage cheese to blender, blend on high speed until smooth, about 1 minute, scraping down sides of blender jar as needed. Add 1 egg to blender blend until just combined. Whisk remaining 11 eggs in a bowl with a pinch of salt. Pour cottage cheese mixture into the bowl with the eggs and whisk to fully combine.
Divide the grated cheddar cheese and bacon evenly among prepared muffin cups. Pour egg mixture over filling (cups will be very full). Use skewer or butter knife to carefully stir each muffin cup to evenly disperse fillings and remove air bubbles.
Transfer muffin tin to baking sheet in oven and pour enough boiling water onto baking sheet to fully cover bottom. Bake until sides have begun to pull away from muffin tin and centers are set. Internal temperature should register 170 to 175 degrees, about 25 minutes.
Transfer muffin tin to wire rack and remove eggs muffins from muffin tin as soon as they are cool enough to handle. Serve right away, or allow to cool completely and then store in an air tight container in the refrigerator for up to 5 days. Reheat egg muffins in the microwave for 30 seconds.