Whisk the eggs, milk, salt and pepper to taste in a large bowl and set aside.
Add olive oil to a skillet over medium heat, followed by the bell pepper and chopped broccoli. Add a little salt and pepper. Cook for 5-10 minutes until the broccoli is bright green and fork-tender.
Pour the whisked eggs into the pan and stir. Cook over medium/low heat until eggs are just cooked through, stirring occasionally to scramble them, about 5 minutes. Turn off the heat and fold in the shredded cheese until it's melted. Transfer the egg mixture to a plate and let it cool for 20 minutes. Wipe the pan out and return to the stove.
Assemble the burritos. Place 1/3 of the egg and veggie mixture on a tortilla. See the video above for proper rolling instructions! Repeat two more times.
Optional step to seal the burritos: heat up the skillet with a very small amount of oil spread in a thin layer. Place the burritos seam side down and let them cook for 3-4 minutes on medium/high heat. This will help the burritos stay together!
Let the burritos cool then store in an airtight container or wrapped in foil, plastic wrap or beeswax wrap. Then place in the fridge.