Step 1

In a medium skillet over medium heat, add the butter and the oil and heat, while stirring, until the butter is melted.

Step 2

Add the onions, the thyme, the salt, and the pepper to the butter mixture and cook, stirring occasionally, until the onions are very soft and caramelized, about 15 minutes.

Step 3

Increase the heat to medium-high and cook the onions, stirring occasionally, until they become more golden in color, about 5 minutes.

Step 4

Pour the cooked onions into a small bowl and let them cool completely.

Step 5

Preheat the oven to 350 degrees F.

Step 6

Line a baking sheet with parchment paper.

Step 7

Cut each of the ham slices into 3 (2x5-inch) strips.

Step 8

Cut the brie into 24 (1/4x1-inch) pieces.

Step 9

On each of the ham strips, add 1/4 teaspoon of the caramelized onions and 1 of the brie pieces.

Step 10

Tightly roll up each of the strips.

Step 11

On a cutting board, separate the crescent dough at the perforations into 8 triangles.

Step 12

Cut each of the dough triangles into 3 long, thin triangles, making 24 dough triangles total.

Step 13

Lay 1 of the ham rolls centered on the small tip end of each of the dough triangles and roll them up until you reach the wide, flat end of the dough triangle.

Step 14

Place the ham rolls seam-side down on the prepared baking sheet.

Step 15

Evenly top each of the ham rolls with the remaining caramelized onions.

Step 16

Bake the ham rolls until the dough is golden-brown and cooked through, about 25-30 minutes.

Step 17

Serve the pigs with the Dijon mustard.