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1
Heat the butter and oil in a medium skillet over medium heat.
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2
Add the onions, thyme, 1/2 teaspoon salt and a few grinds of pepper, and cook, stirring occasionally, until the onions are very soft and caramelized, about 15 minutes.
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3
Raise the heat a little, and cook to develop a more golden color, about 5 minutes more.
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4
Transfer the onions to a small bowl to cool completely.
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5
Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper.
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6
Cut each slice of ham into 3 strips about 2 inches by 5 inches.
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7
Cut the Brie into 24 pieces about 1/4 inch by 1 inch.
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8
On each strip of ham, place 1/4 teaspoon of the caramelized onions and 1 piece of Brie, and roll up tightly.
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9
Open the tube of dough, and separate it into 8 triangles at the perforations.
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10
Cut each triangle into 3 long, thin triangles (for 24 pieces total).
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11
Lay 1 ham roll centered on the tip end of a triangle, roll until you reach the flat end and place, seam-side down, on the prepared baking sheet.
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12
Repeat with the remaining triangles and ham rolls.
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13
Top each finished roll with a dab (about 1/8 teaspoon) of the remaining onions.
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14
Bake until the dough is golden brown and cooked through, 25 to 30 minutes.
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15
Serve warm with Dijon mustard on the side.
