Position a rack in the bottom third of the oven. Preheat oven to 400 F.
Butter a 2 1/2-cup cocotte with 1/2 tablespoon of butter. Dust with the Parmesan, tilting to evenly coat the bottom, sides and rim.
In a heavy-bottomed skillet with a lid, heat the oil over medium-high heat. Add the fennel and onion and cook, stirring occasionally, until the vegetables start to brown, about 5 minutes. Lower heat to medium, then cover and cook 5 more minutes. Uncover and add 1 tablespoon of water. Continue to cook, stirring, until golden brown and soft. Remove from the pan and let cool.
In a heavy-bottomed saucepan, melt the remaining tablespoon of butter over medium heat. Add the flour and stir constantly for about 3 minutes, until completely smooth and incorporated. Pour in the milk in a thin stream, while whisking constantly. Continue to cook over medium heat, whisking all the while, until the sauce thickens, about 5 to 10 minutes. Remove from the heat and whisk in the salt.
Drop in the egg yolks one at a time, whisking well after each addition. Use a silicone spatula to scrape the souffle base into a large bowl. Stir in the cooled vegetables, bacon bits and chives.
With an electric mixer, beat the egg whites until shiny and stiff, but not dry. Use a silicone spatula to fold a quarter of the egg whites into the souffle base.
Fold in the remaining whites in two additions, while gradually sprinkling in the cheese. Take care not to deflate the egg whites. Pour the mixture into the buttered cocotte.
Set the cocotte on a baking sheet and place in the oven. Immediately lower the heat to 375 F. Bake until puffy and golden and very slightly jiggly in the center, about 25 to 30 minutes. Test with a skewer if desired; it should come out fairly dry. Serve immediately.