Heat oil in a small saucepan over medium heat until shimmering.
Add shallot rings and fry, stirring occasionally, until deeply golden and crispy — about 5-7 minutes.
Remove with slotted spoon to paper towels. Season immediately with kosher salt.
Pour aged balsamic vinegar into a small pan over medium-low heat.
Simmer until reduced by half and syrupy — about 5-7 minutes.
Remove from heat.
Tear burrata into pieces and drape onto each cracker.
Pile crispy shallots on top.
Drizzle with balsamic glaze.
Tuck fresh raspberries into the pile.
Finish with flaky sea salt.