Place the two eggs in a small pot and cover with cold water. Set the pot over medium-high heat, bring to a simmer, then set a timer to 4:30 minutes. (Keep the water to a low simmer, because boiling might crack the eggs.) When done, immediately fish the eggs out of the water and transfer to a bowl filled with ice water. Let cool completely, 5 to 10 minutes. (You can prepare the eggs in advance and store them in their shells, in an airtight container, in the fridge, for up to two days.)
Slice the avocado open vertically, remove the pit, and scoop out the flesh in a shallow bowl or on a plate. Cut the lime in half and squeeze or press out its juice over the avocado. (I like my smashed avocado very lime-y, so if you feel this might be too much for you, start with the juice from half the lime, then add more, to taste.) Use a fork to smash the avocado and mix in the lime juice. Season with fleur de sel and ground pepper to taste.
Carefully peel the eggs and rinse the peeled eggs under running water to make sure no flecks of shell remain. Set the eggs on a paper towel while you prepare the tartines.
Toast both slices of bread. If they are too large to fit into the toaster, toast them in a skillet. Set the toasted slices of bread on two serving plates. Divide the smashed avocado between the two tartines. Top each with one egg sliced in half. Generously sprinkle with toasted pumpkin seeds and dukkah. Drizzle with extra-virgin olive oil and serve immediately.
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