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Combine 2 cups quartered strawberries, 1 tbsp water and 1 tbsp honey in a small sauce pan.
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Stir over medium-low heat for about 5 minutes, until the strawberries begin to soften and release their juice. The strawberries will still remain intact, but be very soft.
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Whisk together the corn starch and remaining tablespoon water into a smooth slurry, then pour into the saucepan with the cooked strawberries, stirring until the sauce thickens slightly, 1-2 minutes.
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Transfer the jam to a heat-proof bowl and stir in another ½ cup reserved quartered strawberries, saving the remaining for topping. Chill until completely cool.
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Stir together the yogurt, remaining 1 tablespoon honey and vanilla until smooth. Chill until ready to use.
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Divide jam into four 6-ounce ramekins. Top with remaining yogurt, smoothing out the top.
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Working on one ramekin at a time, sprinkle yogurt with enough sugar to coat into a thin, even layer, about 1 teaspoon.
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Use a kitchen blow torch to create the brûlée shell. Hold the torch a few inches away from the sugar to gently caramelize, using a swirling motion to keep it from getting too dark in any one area.
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Repeat with a second layer of sugar over the first to create a thick caramelized sugar lid.
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Chill for 10 to 15 minutes to harden the sugar on top and cool the yogurt.
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Top with remaining fresh strawberries and serve immediately.