In a medium pot, cover the beef with water and season with 1½ tsps. of salt, onion, garlic, and bay leaves. Bring to a simmer at medium heat. Continue cooking the beef until it shreds easily with two forks. This could take up to 1 hour. When ready, remove beef from the water and shred while meat is still warm. Set it aside.
While the beef cooks, prepare the avocado salsa. Add all the ingredients to the blender. Blend on high until smooth and creamy. Transfer to serving dish and cover directly with plastic wrap. Keep chilled until ready to serve.
Brush the tortillas lightly with oil on each side. Stack the tortillas and place them into a plastic storage bag. Fold the top of bag down, do not seal, and microwave on high for 1 minute.
Take about 2 tablespoons of beef and fill the softened tortilla on the side closest to you. Roll as tight as you can and set seam side down. Repeat until all tortillas are filled. If you are using toothpicks, you can secure three taquitos together, seam sides touching, side by side. Pierce through with two toothpicks towards the center spaced 1 ½ inches apart.
In a medium skillet, preheat 2 1/2 cups of oil for 5 to 7minutes at medium heat. Fry 5 to 6 taquitos at a time, but don't overcrowd the pan. Fry for a few minutes per side or until golden and crispy.
Line a bowl with paper towels and transfer the taquitos in a standing position into bowl to drain. Serve with lettuce, avocado salsa, crumbled Mexican cheese, Mexican crema, and a side of Mexican rice.