Place the sliced tomatoes on a plate, drizzle with balsamic vinegar, and season with salt and pepper. Set aside.
Make the hollandaise sauce: In a high-speed blender, place the cashews, water, olive oil, lemon juice, mustard, garlic, turmeric, salt, and a few grinds of black pepper and process into a smooth sauce. Transfer to a small bowl and set aside. The sauce can be made in advance and stored in the fridge.
Make the poached eggs: Crack the first egg into a small bowl. Heat a medium pot of water until bubbles form on the bottom of the pan but the water is not yet boiling. Add a few splashes of white vinegar. Stir the water so that it moves in a circular motion. Gently drop the egg into the water, give the water one more gentle stir, then set a timer for 4 minutes. Scoop the egg out of the water. Test the egg for doneness and determine if you need more or less time per egg. Continue with the remaining eggs. If you are comfortable with the technique, you can poach two at a time.
To assemble: When you are ready to serve, check the sauce, if necessary, stir in a tiny bit of water so it's a thick but drizzleable consistency. Assemble each plate with two halves of the toasted English muffins and top each half with a tomato slice, a basil leaf, a poached egg, and a generous drizzle of the sauce. Season with salt and pepper to taste, top with fresh chives, and serve immediately.
The sauce will keep in the fridge for up to 5 days. Recipe from Love & Lemons Every Day by Jeanine Donofrio.