Place a steamer basket into a large pot and add enough water to come up to the bottom of the basket. Place the pot over high heat and bring to a boil.
Nestle the mussels in the basket and cover the pot. Adjust the heat to maintain a simmer and cook for about 3 minutes until the mussels open and are just barely cooked through and still tender. Remove from the heat.
In a small bowl, combine the butter, garlic oil, dill, and lemon juuice. Using a fork, mash everything to combine.
Discard any mussels that have not opened. Break the mussel shells apart and place the half containing the mussel on a large baking sheet. Distribute the dill butter among the mussels. This is messy work and will likely require your hands; don't get too fussy about perfection.
Broil for about 2 minutes until the butter melts and the mussels are warmed through.
Bottled garlic oil is worth keeping on hand for its ease and a flavor that is distinctly garlicky without being overpowering. If you can't find it, use olive oil and add 1 garlic clove, freshly minced, to the dill butter.
Keyword 30 minutes or less, dill, gluten-free, mussels