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1
Heat a cast-iron or heavy-bottomed skillet over medium until the skillet is good and hot. I test either by hovering my hand over (not touching! don't touch!) the skillet, or flicking a drop of water in. When the droplet sizzles and scatters across the skillet, it's ready.
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2
Meanwhile, generously butter each half of the baguette. Don't skimp, you'll be using the residual butter to heat the chicken and fry the eggs. When skillet is hot, place the baguette halves in, butter-side down, and grill until golden brown and crispy, about 5 minutes.
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3
Remove the baguettes from the skillet and place on the plates you'll be eating off of.
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4
Turn the heat to medium-low and add the chicken (you can use more or less than 1.5c, depending on how meaty you want your sandwich). Saute until warm, about 3 minutes. Remove to a separate plate (to prevent the nice crispy bread from getting soggy).
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5
If your pan is looking a little light on oil at this point, add a quick glug (1-2 teaspoons should do it) of olive oil. Crack the eggs into the pan and fry to desired doneness (I like my yolks nice and runny, which takes about 3 minutes with a pre-warmed pan).
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6
While the eggs are frying, assemble the rest of the sandwich. Mustard (if you're using it), then chicken, then arugula (so it wilts a little, between the warm chicken and the warm eggs).
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7
Once eggs are finished, lay one on top of each sandwich.
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8
Grate parmesan over each sandwich, and then top with anchovies, if you so choose (I always do, we are unrepentant anchovy-lovers in my family). Salt and pepper to taste (depending on how seasoned your roast chicken is, you may want more or less of this).
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9
Enjoy! If I'm feeling particularly indulgent, I serve this as a mid-day meal with a good, dry white wine.
