For the vinaigrette, thinly slice kumquats (no need to remove seeds), and place in a medium bowl. Add sliced shallots, garlic, vinegar, olive oil, honey, and cilantro. Whisk to combine. Allow to rest for at least 1 hour.
For the gougères, preheat oven to 375°F. Place the butter and water in a small saucepan over medium heat. Once the butter has melted, add the flour and whisk vigorously until there is no visible flour remaining. Add one egg at a time, fully mixing before adding another. Once the dough is completely combined, add the Gruyère and mix to distribute. Divide the batter evenly into a popover pan and bake for 35-40 minutes until golden brown.
While the gougères are baking, preheat a cast-iron skillet over medium-high heat. Add 2 Tbsp of olive oil. Cut avocados in half and remove the pits. Leaving the skin on, place cut sides down into the skillet and cook for 3-4 minutes or until deep golden brown. Set aside and allow to cool.
Separate each leaf of lettuce and place into a large bowl. Using a mandolin, thinly slice the radishes. (I like to slice them lengthwise and leave some of the green stem attached.) Add to the bowl with lettuce. Using a large spoon, scoop out the cooled avocado flesh and place on a cutting board. Cut into ½-inch irregular shapes. Toss lettuce with half of the vinaigrette. Arrange on a platter or individual plates and top with avocado. Serve with additional vinaigrette on the side and warm gougères.