To make the pesto & sun-dried tomato marinated burrata:
Drain the burrata and add the pesto and olive oil. Stir to combine and allow to sit for at least 20-30 minutes.
To make the whipped herbed goat cheese:
Place the goat cheese, herbs, and olive oil in a small bowl and whip with a small whisk. Drizzle with olive oil and sprinkle with crushed red pepper.
To make the spicy pickled carrots:
In a medium-sized bowl, combine the carrots, jalapeños, and onions. Distribute the vegetables between 2 clean largemouth canning jars, making sure there is at least 1/2 inch remaining at the top of each jar. Add 1/2 of the garlic, 1 bay leaf, and 1 thyme sprig to each jar.
Place the vinegar, water, salt, oregano in a small saucepan over high heat. Bring to a boil, stirring to dissolve the salt. Pour the hot brine into the jars, leaving 1/2 inch at the top. (You might not use all the brine.) Gently tap the jars against the counter a few times to remove all the air bubbles. Top off with more pickling brine if necessary.
Place the lids over the jars and screw on the rings until tight. Let the jars cool at room temperature for at least 1 hour. Store the pickles in the refrigerator. The pickles will improve with flavor as they age — try to wait at least 24 hours before opening.