In a mixing bowl, combine the unsalted butter, minced garlic, chopped parsley, and salt. Mix until well combined and creamy. Set aside.
If you're making sandwiches, slice the large soft rolls in half. For hors d'oeuvres, use a cookie cutter to cut 24 circles out of your sandwich bread.
Generously spread the garlic butter mixture on the cut sides of the rolls or on the rounds of bread.
Slice the brie into thick pieces and layer them on one side of each roll or on half of the bread rounds.
Add a layer of thinly sliced cucumbers and onions. The freshness of these vegetables will brighten the rich flavors of the brie and garlic butter.
Spread a thin layer of mayonnaise on the other side of the rolls or on the remaining bread rounds.
Close the sandwiches by placing the other half of the roll on top or add another round of bread if making hors d'oeuvres.
For a warm, melty experience, you can toast the assembled sandwiches on a skillet or in a panini press until the bread is golden and the brie is slightly melted.
Slice the sandwiches into halves or quarters if desired, or serve the hors d'oeuvres as is on a platter. Enjoy them warm or at room temperature!