In a deep skillet, add oil and bring the temperature to 375ºF.
Slice the beef against the grain to about a ¼-inch thick and 3-inches long; set aside.
In a medium mixing bowl, add cornstarch, water and eggs; whisk until nice and smooth.
Add the beef strips to the batter and coat well. Set aside until the oil reaches temperature.
Meanwhile, in a small bowl, add all the sauce ingredients and whisk until blended and the sugar is mostly dissolved; set aside.
When the oil temperature reaches 375ºF, working in batches, carefully add the battered meat and fry until crispy, about 3 to 4 minutes.
Using a spider strainer, transfer the fried strips to a plate and set aside while working with the remaining ones.
In a wok over medium-high heat, add a ¼ cup of oil. When it starts shimmering, add the carrots and sauté for 1 ½ to 2 minutes or until they start getting soft.
Add peppers and sauté them until just tender, about 2 to 2 ½ minutes.
Add minced ginger and pressed garlic; sauté for 30 seconds.
Pour in the sauce, stir very well to coat and bring the mixture to a rapid simmer before adding the cornstarch mixture; stir until the sauce thickens.
Add the fried strips and stir to coat. Continue stirring to warm up the beef, about 1 to 2 minutes.
Serve immediately over a bed of rice and garnish with sesame seeds and chopped green onions.