Make the Orange Lavender Fig Jam and place it in the fridge to cool down while you prepare the rest of the ingredients.
Position a rack 4 to 6 inches from the heat and preheat the oven to broil.
In a bowl, whisk the eggs with the salt and pepper. Toast the English muffins until golden brown and set aside.
In a large nonstick skillet, heat the butter over medium-high heat. When the butter begins to foam and sizzle, pour the eggs into the pan. As the bottom begins to cook, lift up the outside of the eggs with a heatproof spatula so that the runny center flows to the sides of the pan. When the bottom is fully cooked–about 30 seconds–carefully flip the eggs so that they’re now top-side down. If you’re not comfortable flipping the eggs, scramble them with the spatula until soft and fluffy. Immediately remove the eggs from the heat and divide into 4 portions.
Spread all 8 toasted English muffin halves with fig jam. Top 4 of the halves with even portions of scrambled egg and Taleggio, and place them on a baking sheet. Broil until the cheese is melted, about 45 seconds. Top the melted cheese with arugula and the other half of the English muffin.