Place a large nonstick saute pan over medium heat. Add the butter and olive oil to the pan and heat until the butter is melted and the oil is shiny. Add the onions, sprinkle with 1 teaspoon salt and 1/2 teaspoon pepper and stir to combine. Cook, stirring occasionally, until the onions are very soft and golden in color, about 25 minutes. Add the sherry and thyme and cook for 2 minutes more.
Reduce the heat to low and add the goat cheese, half-and-half and lemon zest and juice. Cook, stirring, until the cheese is melted and incorporated into the caramelized onions, about 3 minutes. Add the chopped tarragon and season with salt and pepper.
Prepare the tartlet shells according to the package instructions.
While the filling is still warm, place a heaping tablespoon into each tartlet shell. Drizzle a pea-size drop of honey on each tartlet and top with a tarragon leaf.